41. 2002BCAT 2002 Barcelona Conference on algebraic topology. Barcelona, July 2 to 6, 2002. http://www.2002bcat.org/

2002 Barcelona Conference on Algebraic Topology Barcelona, July 2 to 6, 2002. General information Speakers Schedule Instructions for speakers and posters ... Accommodation Picture of the conference This EuroConference is supported by the European Commission under contract number HPCF-CT-2001-00246 of the improving Human Research Potential Programme.

42. MAT 539 -- Algebraic Topology MAT 539 algebraic topology. Textbook. Differential forms in algebraic topology, by Raoul Bott and Loring W. Tu, GTM 82, Springer Verlag 1982. http://www.math.sunysb.edu/~sorin/topology/home.html

MAT 539 Algebraic Topology Instructor Sorin Popescu (office: Math 4-119, tel. 632-8358, e-mail sorin@math.sunysb.edu Prerequisites A basic introduction to geometry/topology, such as MAT 530 and MAT 531 Textbook Differential forms in algebraic topology , by Raoul Bott and Loring W. Tu, GTM , Springer Verlag 1982. The guiding principle of the book is to use differential forms and in fact the de Rham theory of differential forms as a prototype of all cohomology thus enabling an easier access to the machineries of algebraic topology in the realm of smooth manifolds. The material is structured around four core sections: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes, and includes also some applications to homotopy theory. Other recommended texts: Algebraic Topology: A first Course , W. Fulton, GTM , Springer Verlag 1995 Topology from the Differentiable Viewpoint , J. Milnor, U. of Virginia Press 1965 Algebraic Topology , A. Hatcher (on-line), Cambridge University Press, to appear Characteristic classes , J. Milnor and J. Stasheff, Princeton University Press 1974

43. Poster Project, Algebraic Topology Algebraic Geometry and Topology. How different. Read more about algebraic geometry and algebraic topology in the Mathematical Atlas. http://www.math.sunysb.edu/posterproject/www/materials/i-am-math/alg-top.html

Home Introduction Posters Problems ... The Design Team Algebraic Geometry and Topology How can we tell if two shapes are the same? What if these shapes are not two-dimensional but, say, thirty-three dimensional? Saying if two shapes are the same is a very difficult question, but it turns out that telling if two shapes are not the same is a slightly easier question! What do I mean by this? Suppose you have to meet a stranger at the airport. You've never met this person in your life; you don't want to look silly standing there holding a sign. You know the person you are looking for is five foot five, dark haired, wearing red. Suppose you're at the airport and a six foot blonde giant walks out in a green cowboy outfit. You know this is not the person you are looking for. Now suppose, a very neat five foot five brunette walks out wearing a stylish red jumper. Do you know if this is the person you are looking for? When it comes to wild and wacky shapes it is not easy to attach labels like "red" or "dark haired". This is where algebra comes in. Abstract algebra (like, for example, groups) can be "attached" to some spaces in a natural way; they can function as labels like "red". If two spaces have different algebraic labels, they must be different. Read more about algebraic geometry and algebraic topology in the Mathematical Atlas to I am a Mathematician to Asking the Right Question to Knots

44. Handbook Of Algebraic Topology Publisher's page. Contents, ordering information. http://www.elsevier.nl/locate/hat

Home Site map picswapper("picswap", [/authored_framework/ + "images/topbar_1.jpg", /authored_framework/ + "images/topbar_2.jpg", /authored_framework/ + "images/topbar_3.jpg", /authored_framework/ + "images/topbar_4.jpg", /authored_framework/ + "images/topbar_5.jpg", /authored_framework/ + "images/topbar_6.jpg"], 5000) Advanced Product Search Products Handbook of Algebraic Topology Book information Product description Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book related information Submit your book proposal Other books in same subject area Related publications About Elsevier ... http://books.elsevier.com/elsevier/?isbn=0444817794 Edited by I.M. James , c/o Oxford University, Mathematical Institute, Oxford, UK Description Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics. Contents Foreword. List of Contributors. Homotopy types (H.-J. Baues). Homotopy theories and model categories (W.G. Dwyer, J. Spalinski). Proper homotopy theory (T. Porter). Introduction to fibrewise homotopy theory (I.M. James). Coherent homotopy over a fixed space (K.A. Hardie, K.H. Kamps). Modern foundations for stable homotopy theory (A.D. Elmendorf

45. 2002BCAT Institut d'Estudis Catalans, Barcelona, Spain; 26 July 2002. http://www.crm.es/pastactivities/Act2001-2002/2002Bcat.htm

2002 Barcelona Conference on Algebraic Topology. A EuroConference Dates: July 2 to 6, 2002 Place: I nstitut d'Estudis Catalans, Barcelona Scientific Committee: Jaume Aguadé (UAB) Carles Broto (UAB) Carles Casacuberta (UB) Haynes Miller (MIT) Keynote speakers: Ib Madsen (University of Aarhus) Haynes Miller (MIT) Graeme Segal (University of Oslo) Main speakers: Pete Bousfield (University of Illinois at Chicago) John Greenlees (University of Scheffield) Mark Hovey (Wesleyan University) Ran Levi (University of Aberdeen) John Rognes (University of Oslo) Antonio Viruel (Universidad de Málaga) Grants The CRM can offer a limited number of grants to young researchers covering the registration fee and/or accommodation. The deadline for application is March 29, 2002. VERY IMPORTANT If you apply for Financial Support please do the following steps: Send the Application Form for Financial Support before the deadline (please do not pay the Registration fee). Once you receive the resolution on your Financial Application (April 15 approximately) you will be asked to send the Registration Form and the Payment Form (if necessary).

46. Algebraic Topology algebraic topology. The problems of algebraic topology. The most celebrated geometric open problem in algebraic topology is the Poincar?conjecture. http://www.fact-index.com/a/al/algebraic_topology.html

Main Page See live article Alphabetical index Algebraic topology Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. 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 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.

47. Algebraic Topology algebraic topology. The Nature of algebraic topology. A Fundamental Lemma of algebraic topology. For all simplexes s m i and s m2 j http://www.sjsu.edu/faculty/watkins/algtop.htm

Economics Department Thayer Watkins Algebraic Topology The Nature of Algebraic Topology Both Point Set Topology and Algebraic Topology attempt to describe and analyze the properties of geometric objects which are invariant under continuous mappings. Algebraic Topology does this using an indirect approach. Each geometric object is associated with a set of algebraic structures, usually groups . Questions about the geometric objects are converted into questions about the associated groups. This strategy is analogous to the way transform methods are used to solve differential equations. Laplace and Fourier transforms are used to convert a differential equation into a strictly algebraic equation. Algebraic methods are used to solve for the transform of the solution to the differential equation. The inverse transform is applied to the transform of the solution to get the solution to the differential equation. n Let X be a sphere in 3-space and let Y be a torus also in 3-space. The groups to be constructed are based upon loops that begin and end at some point P outside of X and Y. A loop is just a directed path in which the the beginning point and the end point are the same point. Two loops, x and x , can be added by attaching the beginning part of the second loop to the ending part of the first loop. There is also a zero loop, one that does not leave the point P. The situation is illustrated in the diagram below.

48. Research In Geometry & Algebraic Topology Geometry and algebraic topology. http://www.maths.gla.ac.uk/research/groups/geoalgtop/geoalgtop.html

Mathematics Home Research Undergrad Postgrad ... Mathematical Education In many respects, the latter half of the 20th Century has been a golden age of Geometry and Topology, with spectacular advances in the study of manifolds (particularly in dimension 4), Global Analysis including Index Theory, complex manifolds and Algebraic Geometry, including its applications in Number Theory. Increasingly, strong connections with integrable system theory and global aspects of differential equations as well as the remarkable two-way flow of ideas between Geometry and Theoretical Physics are dominating developments. Algebraic Topology has developed important machinery such as cohomology theories including ordinary cohomology, K -theory, cobordism and elliptic cohomology. These are often of use in geometric situations, as well as within Algebraic Topology itself which tends to study much less `rigid' geometric situations than Geometers do. There have also been significant interactions with many areas of Algebra, and indeed much of Algebraic Topology can be viewed as `applied algebra' as well as being a major source of innovative algebraic ideas. Departmental research activity in Geometry and Topology occurs in the following areas.

49. The Math Forum - Math Library - Algebraic Topology This page contains sites relating to algebraic topology. Browse and Search the Library Home Math Topics Topology algebraic topology. http://mathforum.org/library/topics/alg_topol/

Browse and Search the Library Home Math Topics Topology : Algebraic Topology Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Algebraic Topology - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to algebraic topology, the study of algebraic objects attached to topological spaces. The algebraic invariants reflect some of the topological structure of the spaces. The use of these algebraic tools calls attention to some types of topological spaces which are well modeled by the algebra; fibre bundles and related spaces are included here... the use of the algebraic tools also calls attention to the aspects of a topological space which are well modeled by the algebra; this gives rise to homotopy theory. The algebraic tools used in topology include various (co)homology theories, homotopy groups, and groups of maps. These in turn have necessitated the development of more complex algebraic tools such as derived functors and spectral sequences. History, applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> AT Algebraic Topology (Front for the Mathematics ArXiv) - Univ. of California, Davis

50. Algebra And Algebraic Topology Home Page School of Informatics, Algebra and algebraic topology. http://www.informatics.bangor.ac.uk/public/mathematics/research/algtop/algtop2.h

University of Wales, Bangor - School of Informatics Research Group Home Pages Introduction. The research in algebra at Bangor has to a large extent been motivated by problems in algebraic topology and homological algebra. The recent spate of new and exciting concepts (crossed modules, crossed n-cubes, nonabelian tensor products, etc.) originating in those two areas has opened out many algebraic aspects of the theory and applications which are waiting to be investigated. Many final year pure mathematics courses have some Algebraic Topology in them. Typically the fundamental group and/or the homology groups are defined, studied and applied to various problems such as the existence of certain types of continuous maps, the classification of knots, and other problems of classification usually in low dimensions. These problems usually involve two basic questions: 1. How is one to tell if two spaces or two maps are "different"? 2. Can a map defined on part of a geometric object be extended to the whole of that object? In both cases the method of algebraic topology is to model certain important aspects of each space by some algebraic gadget, perhaps a group or a set of interrelated groups, use these to translate the problem to an algebraic context; try to solve that algebraic problem and finally to reinterpret the results back in terms of spaces.

51. May, J. P.: A Concise Course In Algebraic Topology May, JP A Concise Course in algebraic topology, university press books, shopping cart, new release notification. http://www.press.uchicago.edu/cgi-bin/hfs.cgi/00/13911.ctl

Go to ... Full text search Excerpts Subject catalogs Subject index ... Shopping cart contents or Print an order form May, J. P. A Concise Course in Algebraic Topology . x, 244 p., 117 line drawings. 1999 Series: (CLM) Chicago Lectures in Mathematics Series Paper $20.00tx 0-226-51183-9 Fall 1999 Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field. Subjects: Mathematics and Statistics The University of Chicago Press You may purchase this title at these fine bookstores . Outside the USA, consult our

52. Algebraic Topology Discussion List Information on subscribing, archives of past discussions, and links to home pages of algebraic topologists. http://www.lehigh.edu/dmd1/public/www-data/algtop.html

Algebraic Topology Discussion List This list is maintained by Don Davis. To subscribe or unsubscribe or post a message for the list, send e-mail to dmd1@lehigh.edu. The primary functions of this list are the first three items listed below: providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, and serving as a forum for topics related to algebraic topology. This website also serves as an archive of links to websites related to algebraic topology. The Hopf archive is a preprint server for papers in algebraic topology. It is maintained by Clarence Wilkerson. Every few weeks, Mark Hovey posts abstracts of papers which have been added to the Hopf archive. Information about conferences Other posted messages List of e-mail addresses of people on the list . There are more than 600 subscribers. Links to home pages of algebraic topologists Links to other sites related to algebraic topology (books, journals, tables, research groups, ongoing seminars, other sites) As a new service for the nonspecialist, we have an

53. May, J. P.: Simplicial Objects In Algebraic Topology May, JP Simplicial Objects in algebraic topology, university press books, shopping cart, new release notification. http://www.press.uchicago.edu/cgi-bin/hfs.cgi/00/1470.ctl

Go to ... Full text search Excerpts Subject catalogs Subject index ... Shopping cart contents or Print an order form May, J. P. Simplicial Objects in Algebraic Topology Paper $20.00tx 0-226-51181-2 Spring 1993 Since it was first published in 1967, Simplicial Objects in Algebraic Topology has been the standard reference for the theory of simplicial sets and their relationship to the homotopy theory of topological spaces. J. Peter May gives a lucid account of the basic homotopy theory of simplicial sets (discrete analogs of topological spaces) which have played a central role in algebraic topology ever since their introduction in the late 1940s. Simplicial Objects in Algebraic Topology presents much of the elementary material of algebraic topology from the semi-simplicial viewpoint. It should prove very valuable to anyone wishing to learn semi-simplicial topology. [May] has included detailed proofs, and he has succeeded very well in the task of organizing a large body of previously scattered material." Mathematical Review Subjects: Mathematics and Statistics The University of Chicago Press You may purchase this title at these fine bookstores . Outside the USA, consult our

54. Publication: Handbook Of Algebraic Topology (Elsevier Science) Handbook of algebraic topology. Elsevier Science Complete Catalogue Use the search engine provided to find full descriptive details http://www.elsevier.nl/homepage/saj/525347/Menu.shtml

Handbook of Algebraic Topology Elsevier Science Complete Catalogue Use the search engine provided to find full descriptive details about any of our publications, together with ordering information. Elsevier Science Tables of Contents (ESTOC) The tables of contents for Elsevier Science journals since J anuary 1995. Elsevier Science Home Page Elsevier Science

55. Prof. C.B. Thomas University of Cambridge. Application of algebraic topology to differential geometry. http://www.dpmms.cam.ac.uk/site2002/People/thomas_cb.html

Department of Pure Mathematics and Mathematical Statistics DPMMS People Prof. C.B. Thomas Prof. C.B. Thomas Title: Professor of Algebraic Topology College: Robinson College Room: E1.19 Tel: +44 1223 337970 Research Interests: It has long been known that the existence of certain geometric structures on smooth manifolds imposes topological constraints. A deeper question is to ask whether these suffice, and if not, what additional conditions are needed. Examples include Riemannian metrics (with positive scalar, Ricci or sectional curvatures), contact and symplectic forms. In attempting to solve these problems interesting arithmetic questions arise - for example on the role of cubic forms in the construction of symplectic 6-manifolds. Other interests: group cohomology, geometrisation of 3-manifolds, application of topology to number theory. Information provided by webmaster@dpmms.cam.ac.uk

56. Algebraic Topology - Encyclopedia Article About Algebraic Topology. Free Access, encyclopedia article about algebraic topology. algebraic topology in Free online English dictionary, thesaurus and encyclopedia. algebraic topology. http://encyclopedia.thefreedictionary.com/Algebraic topology

Dictionaries: General Computing Medical Legal Encyclopedia Algebraic topology Word: Word Starts with Ends with Definition Algebraic topology is a branch of mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in Philosophy of mathematics. Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships. Click the link for more information. in which tools from abstract algebra Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. The term "abstract algebra" is used to distinguish the field from "elementary algebra" or "high school algebra" which teaches the correct rules for manipulating formulas and algebraic expressions involving real and complex numbers. Historically, algebraic structures usually arose first in some other field of mathematics, were specified axiomatically, and were then studied in their own right in abstract algebra. Because of this, abstract algebra has numerous fruitful connections to all other branches of mathematics.

57. Algebraic Topology -- From MathWorld Index to articles on algebraic topology. http://mathworld.wolfram.com/topics/AlgebraicTopology.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Topology Algebraic Topology Abstract Simplicial Compl... Homotopy Simplicial Complex Link Algebraic Topology ... Wild Point

58. List Of Algebraic Topology Topics - Encyclopedia Article About List Of Algebraic encyclopedia article about List of algebraic topology topics. List of algebraic topology topics in Free online English dictionary, thesaurus and encyclopedia. http://encyclopedia.thefreedictionary.com/List of algebraic topology topics

Dictionaries: General Computing Medical Legal Encyclopedia List of algebraic topology topics Word: Word Starts with Ends with Definition This is a list of algebraic topology Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. 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 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. Click the link for more information. topics , by Encyclopedia page. Homology (mathematics) A separate article treats homology in biology. In mathematics (especially algebraic topology and abstract algebra), homology is a certain general procedure to associate a sequence of abelian groups or modules to a given mathematical object. See homology theory for more background. Construction of homology groups The procedure works as follows: Given the object Click the link for more information.

59. MathGuide: Algebraic Topology MathGuide algebraic topology (15 records). Subject Class, Algebraic geometry; Global analysis, analysis on manifolds; algebraic topology. http://www.mathguide.de/cgi-bin/ssgfi/anzeige.pl?db=math&sc=55

60. The Kenzo Program. A computer program for computational algebraic topology. http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/

Overview. The Kenzo program is the last version (16000 Lisp lines, July 1998) of the CAT (= Constructive Algebraic Topology) computer program. Kenzo is also the name of my cat . The Kenzo program is a joint work with Xavier Dousson. The previous version EAT (May 1990) was a joint work with Julio Rubio. The Kenzo program is significantly more powerful than EAT, from several points of view. On one hand, for the computations which could be done with the EAT program, the computing times are divided by a factor generally between 10 and 100. The reasons are multiple and it is not obvious to decide what the most important are. Some are strictly technical; for example the numerous multi-degeneracy operators are now coded with a unique integer, using an amusing binary trick: various tests show much progress has been obtained in this way. Other reasons are strictly mathematical; for example another choice for the Eilenberg-Zilber homotopy operator leads in the Kenzo program to Szczarba's universal twisting cochain; in the EAT program we used Shih's universal twisting cochain; experience shows that Szczarba's cochain is considerably more efficient than Shih's one. It is a major mathematical problem to understand

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