1. AMS Online Books/COLL27 algebraic topology. by Solomon Lefschetz. Publication Date 1942 Number of Pages 389 pp. Publisher AMS ISBN 08218-3397-9 COLL/27.E Order Book. http://www.ams.org/online_bks/coll27/

Title List Help AMS Home AMS Bookstore Algebraic Topology by Solomon Lefschetz Publication Date: 1942 Number of Pages: 389 pp. Publisher: AMS ISBN: 0-8218-3397-9 COLL/27.E Download Individual Chapters FREE (10 files - 41.5mb) Frontmatter Title Contents Preface Introduction to General Topology Additive Groups Complexes Complexes: Products. Transformations. Subdivisions ... Endmatter Appendices Bibliography and Indexes Comments: webmaster@ams.org Privacy Statement Search the AMS

2. Allen Hatcher's Homepage Contains textbooks in algebraic topology, KTheory, and 3-Manifolds. http://www.math.cornell.edu/~hatcher/

Allen Hatcher Office: 553 Malott Hall Phone: (607)-255-4091 E-mail . The address is hatcher@math.cornell.edu Cornell Math Dept Homepage Cornell Topology Festival Remington Brook - photos On This Webpage: Book Projects: Algebraic Topology Vector Bundles and K-Theory Spectral Sequences in Algebraic Topology ... Books by other authors Book Projects Real and Imaginary Algebraic Topology This is the first in a series of three textbooks in algebraic topology having the goal of covering all the basics while remaining readable by newcomers seeing the subject for the first time. The first book contains the basic core material along with a number of optional topics of a relatively elementary nature. The other two books, which are largely independent of each other, are provisionally titled "Vector Bundles and K-Theory" and "Spectral Sequences in Algebraic Topology." These are only partially written see below. To find out more about the first book or to download it in electronic form, follow this link to the download page Vector Bundles and K-Theory The plan is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes. For further information, and to download the part of the book that is written, go to

3. Algebraic Topology Discussion List The primary functions of this list are 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. The site also serves as an archive of links to websites related to algebraic topology. http://www.lehigh.edu/~dmd1/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

4. 55: Algebraic Topology In Dave Rusin's Mathematical Atlas. http://www.math.niu.edu/~rusin/known-math/index/55-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 55: Algebraic topology Introduction Algebraic topology is 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; fiber bundles and related spaces are included here, while complexes (CW-, simplicial-, ...) are treated in section 57. Finally, 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; the machinery (mostly derived from homological algebra) is powerful if rather daunting. In all cases, the "naturality" of the construction implies that a map between spaces induces a map between the groups. Thus one can show that no maps of some sort can exist between two spaces (e.g. homeomorphisms) since no corresponding group homomorphisms can exists. That is, the groups and homomorphisms offer an algebraic "obstruction" to the existence of maps. Classic applications include the nonexistence of retractions of disks to their boundary and, as a consequence, the Brouwer Fixed-Point Theorem. (Obstruction theory is, more generally, the creation of algebraic invariants whose vanishing is necessary for the existence of certain topological maps. For example a function defined on a subspace Y of a space X defines an element of a homology group; that element is zero iff the function may be extended to all of X.)

5. Algebraic Topology And Concurrency Reports applying methods in algebraic topology to concurrent computation. Maintained by Stefan Sokolowski. http://www.ipipan.gda.pl/~stefan/AlgTop/reports.html

Reports For more up to date versions and for more complete listing of reports see the authors' home pages S. Blanc, Rachid Guerraoui , K. Hess, Petr Kouznetsov , P. E. Parent, Bastian Pochon , O. Sauvageot. Using the Topological Characterization of Synchronous Models. Preliminary Proceedings of GETCO 2002, Toulouse, France, BRICS Notes NS-02-5 , 13 pages. October 2002. Ulrich Fahrenberg Ditopology. Part 2 (pages 45-63) in Geometry and Topology by Ulrich Fahrenberg and John-Josef Leth. Student Project, Dept. of Mathematical Sciences, Aalborg University, Aalborg, Denmark. Ulrich Fahrenberg Towards an Efficient Algorithm for Detecting Unsafe States in Timed Concurrent Systems. M.Sc. thesis, Dept. of Mathematical Sciences, Aalborg University, Aalborg, Denmark. Lisbeth Fajstrup Dicovering spaces. Report R-01-2023, Dept. of Mathematical Sciences, Aalborg University, Aalborg, Denmark. November 2001. Lisbeth Fajstrup , Eric Goubault , Martin Raussen Algebraic Topology and Concurrency. To appear in Theoretical Computer Science . Also preprint R-99-2008, Dept. of Mathematical Sciences, Aalborg University, Aalborg, Denmark.

6. AT Algebraic Topology Preprints in algebraic topology. http://front.math.ucdavis.edu/math.AT

Fri 4 Jun 2004 Search Submit Retrieve Subscribe ... iFAQ AT Algebraic Topology Calendar Search Authors: All AB CDE FGH ... U-Z New articles (last 12) 3 Jun math.AT/0406037 The cone length and category of maps: pushouts, products and fibrations. Martin Arkowitz (Dartmouth College), Donald Stanley (University of Regina), Jeffrey Strom (Western Michigan University). 32 pages. AT 28 May math.AT/0405525 Andrew Baker , Birgit Richter . 6 pages. Glasgow University Mathematics Department preprint no. 04/20. AT AC Cross-listings 2 Jun math.DG/0406008 Boundary case of equality in optimal Loewner-type inequalities. Victor Bangert , Christopher Croke , Sergei V. Ivanov , Mikhail G. Katz . 20 pages. DG AT GT MG 1 Jun math.AG/0405589 Weights in cohomology and the Eilenberg-Moore spectral sequence. Matthias Franz , Andrzej Weber . 14 pages. AG AT 27 May math.GT/0405502 Knot theory in handlebodies. Reinhard Haering-Oldenburg , Sofia Lambropoulou . 23 pages. J. Knot Theory and Ramifications , Vol. 11, No. 6, pp. 921943 (2002). GT AT 27 May math.GT/0405493 Algebraic Markov equivalence for links in 3-manifolds. Sofia Lambropoulou , Colin P.

7. Open Problems In Algebraic Topology Problems in algebraic topology, listed by Mark Hovey, mathematician at Wesleyan University. Mark Hovey s algebraic topology Problem List. http://claude.math.wesleyan.edu/~mhovey/problems/

Mark Hovey's Algebraic Topology Problem List This list of problems is designed as a resource for algebraic topologists. The problems are not guaranteed to be good in any wayI just sat down and wrote them all in a couple of days. Some of them are no doubt out of reach, and some are probably even worseuninteresting. I ask that anybody who gets anywhere on any of these problems, has some new problems to add, or has corrections to any of them, please keep me informed (mhovey@wesleyan.edu). If I mention a name in a problem, it might be good to consult that person before working too hard on the problem. However, even if the problems we work on are internal to algebraic topology, we must strive to express ourselves better. If we expect our papers to be accepted in mathematical journals with a wide audience, such as the Annals, JAMS, or the Inventiones, then we must make sure our introductions are readable by generic good mathematicians. I always think of the French, myselfI want Serre to be able to understand what my paper is about. Another idea is to think of your advisor's advisor, who was probably trained 40 or 50 years ago. Make sure your advisor's advisor can understand your introduction. Another point of view comes from Mike Hopkins, who told me that we must tell a story in the introduction. Don't jump right into the middle of it with "Let E be an E-infinity ring spectrum". That does not help our field. Here are the problems: Major problems in the field Morava K- and E-theory Elliptic cohomology Applications ... Miscellaneous Unstable modules and algebras over the Steenrod algebra (coming soon)

8. Algebraic Topology And Distributed Computing Powerpoint tutorials by Maurice Herlihy at Brown University. http://www.cs.brown.edu/people/mph/topology.html

Algebraic Topology and Distributed Computing Page PowerPoint Tutorial Distributed and concurrent systems Protocols read/write memory decidability

9. What Is Algebraic Topology? WHAT IS algebraic topology? THE BEGINNINGS OF algebraic topology. The winding number of a curve illustrates two important principles of algebraic topology. http://www.math.rochester.edu/people/faculty/jnei/algtop.html

WHAT IS ALGEBRAIC TOPOLOGY? THE BEGINNINGS OF ALGEBRAIC TOPOLOGY Algebraic topology is a twentieth century field of mathematics that can trace its origins and connections back to the ancient beginnings of mathematics. For example, if you want to determine the number of possible regular solids, you use something called the Euler characteristic which was originally invented to study a problem in graph theory called the Seven Bridges of Konigsberg. Can you cross the seven bridges without retracing your steps? No and the Euler characteristic tells you so. Later, Gauss defined the so-called linking number, a precise invariant which tells you whether two circles are linked. It is called an invariant because it remains the same even if we continuously deform the geometric object. Gauss also found a relationship between the total curvature of a surface and the Euler characteristic. All of these ideas are bound together by the central idea that continuous geometric phenomena can be understood by the use of discrete invariants. The winding number of a curve illustrates two important principles of algebraic topology. First, it assigns to a geometric odject, the closed curve, a discrete invariant, the winding number which is an integer. Second, when we deform the geometric object, the winding number does not change, hence, it is called an invariant of deformation or, synomynously, an invariant of homotopy.

10. Index Of /~mischaik/courses/Math4432 Book by T. Kaczynski, K. Mischaikow, and M. Mrozek in PostScript. http://www.math.gatech.edu/~mischaik/courses/Math4432/

Index of /~mischaik/courses/Math4432 Name Last modified Size Description ... math4432.html 05-Apr-2000 11:13 1.1K Apache Server at www.math.gatech.edu Port 80

11. AMS Summer 1999 Research Conference In Algebraic Topology University of Colorado, Boulder, USA; 2024 June 1999. Photos, proceedings. http://www.math.wayne.edu/~rrb/Summer99/

1999 AMS-IMS-SIAM Summer Research Conference on HOMOTOPY METHODS IN ALGEBRAIC TOPOLOGY WHEN: Sunday, June 20 - Thursday, June 24, 1999 (check in June 19, check out June 25) WHERE: University of Colorado , Boulder, CO Now that the conference is over, this web page will be maintained for a time as a source of information about the conference and about the proceedings of the conference. (Which should be appearing any day now.) Here are some photos from the banquet, taken by Donna Salter of the AMS. Here is a copy of the conference photo . It is a 700500 byte jpeg, 3000 x 2187 pixels in size, which takes 10 to 20 minutes to download on my 28 K line. Note that the upper left corner is quite dark: there is nothing wrong with your browser. Scroll down and right to see the people in the photo. Here is a cropped version which is only 532849 bytes, 1265 x 436 pixels in size, and which appears much smaller for some reason known only to XV, the program used to crop it. This is the schedule of talks as they actually occurred, and an alphabetical list of speakers (with titles and abstracts), and the

12. Hopf Topology Archive, Revised Version Seminars at Purdue. algebraic topology Discussion Group Archives maintained by Don Davis. HTTP uploading of submissions. Newer Photographs on Hopf. Time capsule http://hopf.math.purdue.edu/pub/hopf.html

Hopf Topology Archive Welcome to the Hopf Topology Archive! Hopf Author/Title Search: enter author or title keyword into box below. PaperSearch The Hopf Logos The Hopf Archive, month by month listing. CDROM of current Hopf Archive (April 4, 2002) (650MB ) This archive list is current through July. Newer files may be in the proper directories but not listed on the html list. These are accessible as http://hopf.math.purdue/AuthorName <- usually last names of authors. If you have a submission that has not been announced or posted and some time has elapsed, please email Mark and Clarence (but please try the "Reload" button on your browser first. Thanks, Clarence) Hopf has been upgraded to faster CPU and disk. Hope it helps the service. Also, HTTP uploading (http://hopf.math.purdue.edu/upload.php) has been added. Clarence What's New! Nishida Conference Pictures from Prof. V. Tsukiyama,Shimane U. Nishida Conference Pictures from Clarence Wilkerson Uploading Preprints Latest maintained by Mark Hovey. Back issues of Mark's What's New!

13. Allen Hatcher Allen Hatcher Allen Hatcher is a professor of mathematics at Cornell University. On his home page, he offers a link to download his book I algebraic topology /I in its entirety. Published in http://rdre1.inktomi.com/click?u=http://www.math.cornell.edu/~hatcher/&y=02B

14. Algebraic Topology From MathWorld algebraic topology from MathWorld The study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, configuration spaces, etc.) that remain http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/AlgebraicTopology.

15. Algebraic Topology Book algebraic topology. To get an idea of what s in the book you can look at the Table of Contents and the Preface. algebraic topology. Pages, PDF. http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Algebraic Topology To get an idea of what's in the book you can look at the Table of Contents and the Preface Printed Version The book was published by Cambridge University Press in 2002. There are two editions: Paperback (ISBN 0-521-79540-0) for US$32. This is now in a third printing, with corrections of some minor errors in the earlier printings. (See farther down this page for a list of corrections.) Hardback (ISBN 0-521-79160-X) for US$90. This has not been reprinted, so it does not include the corrections that are in the reprintings of the paperback edition. Electronic Version: By special arrangement with the publisher, an online version will continue to be available for download here. Individuals may print out single copies for their own use, but xeroxing multiple copies is not allowed. There are several different formats available. First of all, you can download the whole book as a single rather large pdf file (3.5MB) of about 550 pages. If you wish to save paper when you print it out, there is also a pdf doublepage version with two pages side by side, reduced in size so that they fit on one sheet of paper. Another option is to download the individual chapters as separate pdf files. To get enough material for a one-semester introductory course you could start by downloading just Chapters 0, 1, and 2, along with the Table of Contents, Bibliography and Index. Here are the individual parts:

16. Buy A Concise Course In Algebraic Topology By J. Peter May At A Concise Course in algebraic topology by J. Peter May in Paperback. ISBN 0226511839. algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for http://rdre1.inktomi.com/click?u=http://na.link.decdna.net/n/3532/4200/www.walma

17. Algebraic Topology algebraic topology A short articledesigned to provide an introduction to algebraic topology, the study of algebraic objects attached to topological spaces. The algebraic invariants reflect some of http://rdre1.inktomi.com/click?u=http://mathforum.org/library/view/4261.html&

18. Essays About Algebraic Topology Essays about algebraic topology. What is topology?, by Bob Bruner (Wayne State Univ); What is algebraic topology?, by Joe Neisendorfer (Univ of Rochester); http://www.lehigh.edu/~dmd1/essays.html

Essays about algebraic topology Survey articles for the general public Topology articles from Eric Weisstein's World of Mathematics , sponsored by wolfram.com. Geometry/topology section of Mathematical Atlas , coordinated by Dave Rusin (Northern Illinois Univ) What is topology? , by Bob Bruner (Wayne State Univ) What is algebraic topology? , by Joe Neisendorfer (Univ of Rochester) What is topology? , by Neil Strickland (Univ of Sheffield) Encyclopedia article about topology , by Don Davis (Lehigh Univ) What is Topology (intro to course) , by Zbigniew Fiedorowicz (Ohio State Univ) What is topology , by Kevin Iga (Pepperdine Univ) What is topology , by Jussi Talsi (Finland). History of Topology (early years) , from St Andrews Univ History of Math archive. Algebraic topology entry in Wikipedia (online encyclopedia) Survey articles about topics in topology, written for nonspecialists with some knowledge of mathematics Higher dimensional group theory , by Ronald Brown (Univ of Wales, Bangor) Knot Theory , by knot group at Univ of Wales, Bangor

19. DOE Document - Global Anomalies And Algebraic Topology The algebraic topology aspect of the global pure gauge anomaly calculation is investigated.^In particular, the N), and SO(N) are discussed. Global anomalies and algebraic topology. http://rdre1.inktomi.com/click?u=http://www.osti.gov/energycitations/product.bib

20. Vertex Operators In Algebraic Topology Vertex Operators in algebraic topology This paper is intended for two rather different audiences. First we aim to provide algebraic topologists with a timely introduction to some of the algebraic http://rdre1.inktomi.com/click?u=http://citeseer.ist.psu.edu/307093.html&y=0

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