81. Mathematics 261: Algebraic Topology I . This course is an introduction to algebraic topology.......Mathematics 261 algebraic topology I (Spring 2003). Instructor. Bill Pardon. http://www.math.duke.edu/graduate/courses/spring04/math261.html

Mathematics 261: Algebraic Topology I (Spring 2003) Instructor Bill Pardon Description This course is an introduction to algebraic topology. A rough outline is as follows: Introductory ideas Basic ideas of category theory Homotopy Homotopy of maps Fundemental group Cell complexes Van Kampen's Theorem Covering spaces Higher homotopy groups (very briefly) Homology Chain complexes Simplicial homology Singular homology Relative homology Homotopy invariance Excision Mayer-Vietoris Sequence Cellular Homology Eilenberg-Steenrod Axioms Algebraic topology studies topological spaces by associating to them algebraic invariants. The principal algebraic invariants considered in this course are the fundamental group (also known as the first homotopy group) and the homology groups. This course is a prerequisite for Math 262 (Algebraic Topology II). It is fundamental for students interested in research in Algebraic Geometry, Differential Geometry, Mathematical Physics, and Topology; it is also important for students in Algebra and in Number Theory. Prerequisites Basic algebra (Math 200 or 251) and Topology (Math 205), or consent from me.

82. HMC Math 177a -- Algebraic Topology Math 177a Special Topics algebraic topology Text Munkres, Elements of algebraic topology. Doing the reading will be essential for success in this course. http://www.math.hmc.edu/~su/math177a/

Math 177a Special Topics Algebraic Topology Professor Francis Su x73616, su @ math.hmc.edu Office Hours: WED 1-2:30pm. Course Content: This course is an introduction to algebraic and combinatorial topology, with an emphasis on simplicial and singular homology theory. A major theme in the course will be the connection between combinatorial and topological concepts. Topics will include simplicial complexes, simplicial and singular homology groups, exact sequences, chain maps, diagram chasing, Mayer-Vietoris sequences, Eilenberg-Steenrod axioms, Jordan curve theorem, and additional topics as time permits. This is standard first-year graduate material in pure mathematics. Text: Munkres, Elements of Algebraic Topology . Doing the reading will be essential for success in this course. Prerequisites: Analysis I (Math 131), Algebra I (Math 171), and Topology (Math 147, or topology summer readings), or the permission of the instructor. I will try to set up a few extra sessions to meet with those who did the summer readings. A note about the course: Expect this course to be challenging, but also quite rewarding, as you see the interplay between algebra, topology, combinatorics, and analysis. I will run this course more like a graduate course. As such, I will expect a certain level of mathematical maturity. This means that sometimes I will not prove simple statements in class; you may have to work out some details for yourself or by doing the reading. My focus will be on proving the larger theorems and providing perspective on the material.

83. Algebraic Topology - InformationBlast algebraic topology Information Blast. algebraic topology. algebraic topology is mappings. The problems of algebraic topology. The most http://www.informationblast.com/Algebraic_topology.html

Algebraic topology Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces The goal is to take topological spaces, and further categorize or classify them. An older name for the subject was combinatorial topology , implying an emphasis on how a space X was contructed from simpler ones. The basic method now applied in algebraic topology is to investigate spaces via algebraic invariants: for example by mapping them to groups , which have a great deal of manageable structure, in a way that respects the relation of homeomorphism of spaces. Two major ways in which this can be done are through fundamental groups , or more general homotopy theory , and through homology and cohomology groups. The fundamental groups give us basic information about the structure of a topological space; but they are often nonabelian and can be difficult to work with. The fundamental group of a (finite) simplicial complex does have a finite presentation Homology and cohomology groups, on the other hand, are abelian, and in many important cases finitely generated. Finitely generated abelian groups can be completely classified and are particularly easy to work with.

84. SmartPedia.com - Free Online Encyclopedia - Encyclopedia Books. algebraic topology. Everything you wanted to know about algebraic topology but had no clue how to find it.. Learn about algebraic topology here! http://www.smartpedia.com/smart/browse/Algebraic_topology

Search: Math and Natural Sciences Applied Arts Social Sciences Culture ... Interdisciplinary Categories Algebraic topology Categories Topology Algebraic Topology Abstract algebra Algebraic topology is a branch of mathematics in whichtools from abstract algebra are used to study topological spaces Table of contents 1 The method of algebraic invariants 2 Results on homology 3 Setting in category theory 4 The problems of algebraic topology ... 5 External links The method of algebraic invariants The goal is to take topological spaces, and further categorize or classify them. An older name for the subject was combinatorial topology , implying an emphasis on how a space Xwas contructed from simpler ones. The basic method now applied in algebraic topology is to investigate spaces via algebraicinvariants: for example by mapping them to groups , whichhave a great deal of manageable structure, in a way that respects the relation of homeomorphism of spaces. Two major ways in which this can be done are through fundamentalgroups , or more general homotopy theory , and through homology and cohomology groups. The fundamental groups give us basic information about the structure of a topological space;but they are often

85. Rubriek: 31.61 Algebraic Topology DutchESS, Dutch Electronic Subject Service, Rubriek 31.61 algebraic topology. http://www.kb.nl/dutchess/31/61/

Rubriek: 31.61 algebraic topology Algebraic topology discussion list / Don Davis

86. MA4101 Algebraic Topology MA4101 algebraic topology. MA4101 algebraic topology. Credits 20, Convenor Prof. These ideas, and ones like them, constitute the subject of algebraic topology. http://www.math.le.ac.uk/TEACHING/MODULES/MA-04-05/MA4101.html

Department of Mathematics Next: MA4141 Representations of algebras Up: Previous: MA4041 Methods in Molecular Simulation MA4101 Algebraic Topology MA4101 Algebraic Topology Credits: Convenor: Prof. J.R. Hunton Semester: 2 (weeks 15 to 26) Prerequisites: essential: MA2102 or MA2111, MA2151 desirable: MA3151 Assessment: Coursework: 10% Examination: 90% Lectures: Problem Classes: Tutorials: none Private Study: Labs: none Seminars: none Project: none Other: none Surgeries: none Total: Subject Knowledge Aims This module aims to introduce the basic ideas of algebraic topology and to demonstrate its power by proving some memorably entitled theorems. Learning Outcomes Students should have understood some of the common processes of translating topological or geometric infomation into algebraic information, seeing examples of this through singular and simplicial homology. They should have gained some understanding of the language and techniques of category theory and homological algebra. They will know some of the classical applications of algebraic topology such as the Ham Sandwich theorem, the Hairy Dog theorem and the Borsuk-Ulam theorem. Methods Lectures, example classes, example sheets.

87. Introduction To Algebraic Topology http://www.ualberta.ca/dept/math/gauss/fcm/topology/AlgbrcTop/_00_algtop_frm.htm

88. Algebraic Topology algebraic topology. View a some of disconnectivities play a role. Our EText on algebraic topology. Literature on algebraic topology. http://www.ualberta.ca/dept/math/gauss/fcm/topology/AlgbrcTop/intro1.htm

Algebraic Topology Algebraic topology revolves around to intimately interacting ingredients. These are: The idea of continuously deforming a topological space or, more precisely, deforming a continuous function between topological spaces; Invariants from algebra (groups, rings etc.) associated to a topological space, or a continuous map, which remain unchanged by such deformations. An informal overview Deformations are constrained by the disconnectivities in a space and the associated invariants from algebra constitute "measurements" of these disconnectivities. Let's describe this in some more detail An intuitive discussion of disconnectivities Ideas on how to measure disconnectivities A sample of instances in various parts of mathematics where disconnectivities play a role. Our E-Text on Algebraic Topology Literature on Algebraic Topology Introductory textbooks Advanced textbooks Key papers Miscellaneous c1=" Frequently encountered examples of such invariants are: fundamental group, homotopy groups, homology groups, cohomology rings, Euler characteristic, various flavors of K-theory etc. " The collection of matrices with m rows and n columns " >

89. Algebraic Topology Spring Semester 2004 algebraic topology Spring Semester 2004. Practical information from SIS. Our textbook will be. Allen Hatcher algebraic topology. Cambridge University Press. http://www.math.ku.dk/~moller/f04/algtop/algtop.html

Algebraic Topology Spring Semester 2004 Practical information from SIS . The course will be taught in English. Notes Abstract homotopy theory ( dvi pdf Classification of covering maps ( dvi pdf From singular chains to Alexander duality ( dvi pdf Latest news June 1: I have finished grading your exercises. April 22:Q: Given a (noncontractible) space X does there always exist a (nontrivial) group G that annihilates X in the sense that H_*(X;G)=G. A: No, if X=S^n is the n-sphere, then H_n(S^n;G)=G for all G (Morten) Q: What if one allows chains as coefficients? A: Answer Morten April 20: The dead-line for the homology exercises has been moved to April 29 March 26: I would like to cancel the lecture Tuesday April 6 and instead hold a lecture Tuesday April 13. March 24: Computational Topology March 9: You will get 100 points for all exercises minus 1.3.21 and you will get an extra 25 points if you do 1.3.21 Feb 19: Tuesday and Thursday afternoons are office hours. I will be in my office and you are invited to drop by for a shorter or longer topology chat. Feb 18: The book is again available from the bookstore.

90. MATH 734. Algebraic Topology MATH 734. algebraic topology (Spring 2004). Meeting times MWF, 1100am1150am (MTH 0102) Instructor Professor Jonathan Rosenberg. http://www.math.umd.edu/~jmr/734/

MATH 734. Algebraic Topology (Spring 2004) Meeting times: MWF, 11:00am-11:50am (MTH 0102) Instructor: Professor Jonathan Rosenberg . His office is room 1106 of the Math Building, phone extension 55059, or you can contact him by email . His office hours are Mondays and Fridays 1-2, or by appointment. Texts: Topology and Geometry by Glen E. Bredon , Graduate Texts in Math., vol. 139, Springer-Verlag, Corrected 2nd Printing, 1995, ISBN 0-387-97926-3, and Algebraic Topology by Allen Hatcher, available free on the web , also published by Cambridge University Press in a paperback edition (ISBN 0-521-79540-0) at $32. If you want still another reference that's not too expensive, I'd recommend A Concise Course in Algebraic Topology by J. Peter May , Chicago Lectures in Math., Univ. of Chicago Press, 1999, for $20. It's rather terse but covers everything. Prerequisite: MATH 403 (undergraduate-level abstract algebra). MATH 730 or equivalent is recommended, not 100% necessary if you are willing to take a few facts about the fundamental group on faith. Catalog description: Course Description: Basically, we will cover most of Chapters IV, V, and VI of Bredon, with some of the "starred sections" omitted. Much of this material is also in Hatcher, Ch. 2-3, with a slightly different point of view, and you might find a second presentation helpful.

91. Algebraic Topology Innovations And Patents algebraic topology Innovations and Patents. © 2002, XQ23.COM Research. Recent US patents related to algebraic topology 6,307,551 http://databank.oxydex.com/prospecting_for_knowledge/Algebraic_Topology.html

Algebraic Topology Innovations and Patents © 2002, XQ23.COM Research Recent U.S. patents related to Algebraic Topology: 6,307,551: Method for generating and applying changes in the level of detail of a polygonal surface 6,285,372: Multiresolution adaptive parameterization of surfaces 6,256,603: Performing geoscience interpretation with simulated data 6,128,577: Modeling geological structures and properties 6,052,650: Enforcing consistency in geoscience models 6,031,548: Progressive multi-level transmission and display of triangular meshes 5,966,140: Method for creating progressive simplicial complexes 5,905,657: Performing geoscience interpretation with simulated data 5,850,229: Apparatus and method for geometric morphing 5,784,540: Systems for solving spatial reasoning problems via topological inference 5,667,069: Strengthened handles in membranous articles 5,602,964: Automata networks and methods for obtaining optimized dynamically reconfigurable computational architectures and controls 5,520,282: Strengthened handles in membranous articles

92. 1997 -- Lecture Notes Lecture Notes of the 1997 Summer School FUNDAMENTAL algebraic topology . Ronnie Brown Groupoids and crossed objects in algebraic topology. PostScript file. http://www-fourier.ujf-grenoble.fr/~sergerar/Summer-School/table.html

Lecture Notes of the 1997 Summer School: "FUNDAMENTAL ALGEBRAIC TOPOLOGY" The following lecture notes are available: Clemens Berger: PostScript file. Ronnie Brown: Groupoids and crossed objects in algebraic topology. PostScript file. Sullivan minimal models. Dvi file. Takuji Kashiwabara: Homology of infinite loop spaces and cohomology operations. Dvi and PostScript files. Jean-Louis Loday: Dvi and PostScript files. Lionel Schwartz: Unstable modules and unstable algebras; applications to homotopy theory. Dvi and PostScript files. Francis Sergeraert: Topological constructors. Dvi and PostScript files. Effective homology, a survey. Dvi and PostScript files. Constructive algebraic topology. Dvi and PostScript files. Hans Baues: Homotopy types. Not available here: the lecture notes of Hans Baues' courses was the paper Homotopy Types , pages 1-72 of James' Handbook of Algebraic Topology, North-Holland, 1995. Contents of these papers Clemens Berger: PostScript file.

93. Research Group: Algebraic Topology And Group Theory Algebra and Topology Research Group. http://www.kulak.ac.be/facult/wet/wiskunde/algtop/

Next: Who and where are Sorry, this requires a browser that supports frames! Try index_ct.html instead. Paul Igodt

94. Algebraic Topology (M24) Coherent Sheaves algebraic topology (M24). I. Smith. algebraic topology permeates all of modern pure mathematics. This course http://www.maths.cam.ac.uk/CASM/courses/descriptions/node21.html

Next: Knot Theory (M24) Up: Geometry and Topology Previous: Reading course on the Cohomology of Coherent Sheaves Algebraic Topology (M24) I. Smith Algebraic topology permeates all of modern pure mathematics. This course will introduce several of the basic ideas of the subject, developing them with a slightly geometric flavour. It should however be of interest to people across a broad spectrum. The course will be divided into three (unequal) parts: Homology theory: (co)chain complexes, singular homology, computation methods and axioms. Products in cohomology, cohomology of manifolds. Homotopy theory: homotopy lifting, covering spaces and subgroups of the fundamental group. Higher homotopy groups, the homotopy exact sequence. Characteristic classes: vector bundles and classifying spaces. The Thom isomorphism theorem, the Euler class and applications. Background reading I shall assume that you are familiar with basic analytic topology (topological spaces, compactness, connectedness etc). You can find this material quite concisely in, for example, Introduction to metric and topological spaces by W. A. Sutherland. You should also be confident with linear algebra and quotient spaces, and prepared to look things up!

95. Algebraic Topology algebraic topology. Michaelmas term, 16 lectures Topology is the abstract study of continuity the basic objects of study are metric http://www.maths.cam.ac.uk/undergrad/courseinfo/coursesIIB/text/node6.html

Next: Number Fields Up: COURSES IN PART II(B) Previous: Riemann Surfaces Algebraic Topology Michaelmas term, 16 lectures Topology is the abstract study of continuity: the basic objects of study are metric and topological spaces, and the continuous maps between them. (This course will be concerned exclusively with metric spaces, which were encountered in IB Analysis.) One important difference between topology and algebra is that in constructing continuous maps one has vastly more freedom than in constructing algebraic homomorphisms; thus problems which involve proving the non -existence of continuous maps with particular properties (e.g. the problem of showing that and are not homeomorphic unless m n ) are hard to solve using purely topological methods. The technique that has proved most successful in tackling such problems is that of developing algebraic invariants , which assign to every topological space (in a suitable class) an algebraic structure such as a group or vector space, and to every continuous map a homomorphism of the appropriate kind. Thus questions of the non-existence of continuous maps are reduced to questions of non-existence of homomorphisms, which are easier to solve. Two particular algebraic invariants are studied in this course: the fundamental group, and the simplicial homology groups. Of these, the former is easier to define, but hard to calculate except in a few particular cases; the latter requires the erection of a considerable amount of machinery before it can even be defined, but one this is done it becomes relatively easy to calculate. The course concludes with a classic example of the application of simplicial homology: the classification of all compact 2-manifolds up to homeomorphism.

96. A Concise Course In Algebraic Topology (Chicago Lectures In Mathematics Series(P A Concise Course in algebraic topology (Chicago Lectures in Mathematics Series(Paper)). There is more to this book than just classical algebraic topology. http://www.sciencesbookreview.com/A_Concise_Course_in_Algebraic_Topology_Chicago

A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series(Paper)) A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series(Paper)) by Authors: J. Peter May , Peter J. May Released: June, 1999 ISBN: 0226511839 Paperback Sales Rank: List price: Our price: Book > A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series(Paper)) > Customer Reviews: Average Customer Rating: A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series(Paper)) > Customer Review #1: Lucid and elegant, but not for beginners This tiny textbook is well organized with an incredible amount of information. If you manage to read this, you will have much machinery of algebraic topology at hand. But, this book is not for you if you know practically nothing about the subject (hence four stars). I believe this work should be understood to have compiled "what topologists should know about algebraic topology" in a minimum number of pages. A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series(Paper)) > Customer Review #2: An Outstanding Achievement.

97. Algebraic Topology algebraic topology. algebraic topology by Authors Allen Hatcher Released 15 November, 2001 ISBN 0521795400 Paperback Sales Rank 46,190, http://www.sciencesbookreview.com/Algebraic_Topology_0521795400.html

Algebraic Topology Algebraic Topology by Authors: Allen Hatcher Released: 15 November, 2001 ISBN: 0521795400 Paperback Sales Rank: List price: Our price: Book > Algebraic Topology > Customer Reviews: Average Customer Rating: Algebraic Topology > Customer Review #1: Its worth your money! This book is not just for topologists! If youre like me, then youve spent countless nights sans Hatchers book trying to figure out the fundamental group of a beer can. Look no further, the answers are here! Be sure to check out the vivid detail Hatcher brings to the Van Kampen theorem. Ive not actually read that part myself, as I do not trust german mathematics. Algebraic Topology > Customer Review #2: You would not regret if you buy this. There are many really good textbooks on algebraic topology and each has its own merit: Bredon for his effort in explaining everything that can be dealt without using spectral equences, Fomenko and Novikov for their effort in unifying differential geometry and algebraic/differential topology. Hatchers book is intended as one of the series that cover every aspect of the subject. Separate books on vector bundles and K-theory, and spectral sequences respectively, are to appear sometime in the future. Thus this one covers ordinary homology/cohomology and homotopy theory only. His writing style is helpful and user-friendly, not demanding extensive "mathematical maturity".

98. Algebraic Topology Click to enlarge algebraic topology CRF Maunder. extremely valuable addition to the literature of algebraic topology. The Mathematical Gazette. Unabr. http://store.doverpublications.com/0486691314.html

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Bridge and Other Card Game...... Business and Economics Chess Children Clip Art and Design on CD-...... Cookbooks, Nutrition Crafts Detective, Ghost , Superna...... Dover Patriot Shop Ethnic Interest Features Gift Certificates Gift Ideas History, Political Science...... Holidays Humor Languages and Linguistics Literature Magic, Legerdemain Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy and Religion Photography Posters Puzzles, Amusement, Recrea...... Science and Mathematics Sociology, Anthropology, M...... Sports, Out-of-Door Activi...... Stationery, Gift Sets Stationery, Seasonal Books...... Summer Fun Shop Summer Reading Shop Travel and Adventure Women's Studies By Subject Science and Mathematics Mathematics Topology Algebraic Topology C. R. F. Maunder Our Price (Table of Contents) Availability: In Stock (Usually ships in 24 to 48 hours) Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CW-Complexes and other topics. Each chapter contains exercises and suggestions for further reading. 1980 corrected edition.

99. Algebraic Topology algebraic topology. Although algebraic topology can be considered, by and large, as a creation of the 20th century, it has a long prehistory. http://www.maths.lth.se/matematiklu/personal/jaak/Alg-Top.html

Algebraic Topology Brief historical introduction Although algebraic topology can be considered, by and large, as a creation of the 20th century, it has a long pre-history. It is generally considered to have its roots in Euler's polyhedron theorem (1752). This is the relation $$ E+F=K+2$$ where $E$ is the number of vertices, $K$ the number of edges, and $F$ the number of faces. In the first half of this century many mathematicians defined homology for more and more extended classes of topological spaces. Thus, for instance singular homology was first defined by Lefschetz in 1933. Finally, in 1945, Eilenberg and Steenrod developed an axiomatic approach to homology. It turned out that within the class of all topological spaces the Eilenberg and Steenrod axioms uniquely characterize singular homology. A parallel development took place in homotopy. Thus, higher homotopy groups were defined by Hurewicz in 1935 and their properties were developed. In the 1950's several new concepts were invented such as cobordism and $K$-theory. The course will be based mainly on Greenberg and Harper's book quoted below.

100. Dror Bar-Natan:Classes:2001-02:Algebraic Topology Fundamental Concepts in algebraic topology. Instructor Agenda Learn how algebra and topology interact in the field of algebraic topology. Syllabus http://www.math.toronto.edu/~drorbn/classes/0102/AlgTop/

Dror Bar-Natan Classes Fundamental Concepts in Algebraic Topology Instructor: Dror Bar-Natan drorbn@math.huji.ac.il Classes: Tuesdays 12:00-14:00 at Mathematics 110 and Thursdays 12:00-14:00 at Sprintzak 213. Review sessions: Thursdays 14:00-15:00 with Boris Chorny chorny@math.huji.ac.il Office hours: Tuesdays 14:00-15:00 in my office, Mathematics 309. Agenda: Learn how algebra and topology interact in the field of Algebraic Topology. Syllabus: Prerequisites: Point set topology and some basic notions of algebra - groups, rings, etc. Reading material: (each student must have a copy) Allen Hatcher 's Algebraic Topology (free download; a paper copy is available at my office for photocopying). Weekly Material: (Also use the primitive Class Notes Browser March 12, 14 Class notes for March 12th (the basic idea of algebraic topology, Brouwer's theorem, the fundamental group, the fundamental group of the circle). Homework assignment #1: Ex1.ps Ex1.png (category theory, fundamental group calculations, an application of Brouwer's theorem). Class notes for March 14th (the lifting property for covering spaces, the fundamental theorem of algebra, Brouwer's fixed point theorem)

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