1. Allen Hatcher's Homepage A downloadable textbook in algebraic topology. This is the first in a series of three textbooks in algebraic topology having the goal of covering all http://www.math.cornell.edu/~hatcher/

Allen Hatcher Office: 553 Malott Hall Phone: (607)-255-4091 Math 453, Fall 2005 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

2. AMS Online Books/COLL27 algebraic topology text published by the American Mathematical Society (AMS), and available as a free download in PDF format. © 1942 by Solomon Lefschetz, 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

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 Encyclopedic reference for algebraic topology in Dave Rusin's Mathematical Atlas. Includes a brief history along with various links to textbooks, reference works, and tutorials on the subject. 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. Hopf Topology Archive, Revised Version algebraic topology and related areas. (~400 articles) http://hopf.math.purdue.edu/

Hopf Topology Archive Welcome to the Hopf Topology Archive! NOTICE: Hopf has been moved to a virtual website on the Math department server. Most things should be transparent if you use http://hopf.math.purdue.edu as the URL. The FTP service will not be reactivated due to security concerns. If you experience problems, please report them to wilker@math.purdue.edu Thank you. Hopf Author/Title Search: enter author or title keyword into box below. PaperSearch The Hopf Logos The Hopf Archive, month by month listing. This archive list is current through August 2004 . 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) What's New! CW-Fest: MidWest Topology Seminar honoring Clarence Wilkerson's 60th birthday. Submitting Preprints and Uploading Preprints Latest maintained by Mark Hovey. Back issues of Mark's What's New!

6. Algebraic Topology Book A complete, downloadable, introductory text on algebraic topology, by Prof. Allen Hatcher, Cornell Univ. 3rd Ed. 553 pp. with illustrations. 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). 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. The original price was $30 in the US, but it has now risen to $33. I'm told this is because of the weak dollar. [In April and May 2005 the US amazon.com site had a sale price of $21.77, but now it is back up to $33.] Hardback (ISBN 0-521-79160-X). This has not been reprinted, so it does not include the corrections that are in the reprintings of the paperback edition. The price of the hardback is nearly three times that of the paperback, so it is obviously intended principally for libraries. Electronic Version: By special arrangement with the publisher, an online version will continue to be available for download here. 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

7. 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.

8. AT Algebraic Topology An archive of prepublication papers (preprints) on algebraic topology. http://front.math.ucdavis.edu/math.AT

Fri 16 Sep 2005 Search Submit Retrieve Subscribe ... iFAQ AT Algebraic Topology Calendar Search Authors: All AB CDE FGH ... U-Z New articles (last 12) 15 Sep math.AT/0509293 Lie elements in pre-Lie algebras, trees and cohomology operations. Martin Markl . 20 pages. AT KT 14 Sep math.AT/0509269 Banach Algebras and Rational Homotopy Theory. Gregory Lupton , N. Christopher Phillips , Claude L. Schochet , Samuel B. Smith . 28 pages. AT FA 14 Sep math.AT/0509268 Quasi-commutative cochains in algebraic topology. Max Karoubi . 53 pages. AT KT 12 Sep math.AT/0509213 Self-intersections of Immersions and Steenrod Operations. Peter J. Eccles , Mark Grant . 25 pages. AT 9 Sep math.AT/0509187 Ideal Turaev-Viro invariants. Simon A. King . 16 pages. AT AC Cross-listings 14 Sep hep-th/0509064 Families index theorem in supersymmetric WZW model and twisted K-theory: The SU(2) case. Jouko Mickelsson , Juha-Pekka . 24 pages. ( AT Revisions 13 Sep math.AT/0503613 Dmitry N. Kozlov AT CO 13 Sep math.AT/0502577 Alternative stable homotopy classification of p-completed classifying spaces. Kari Ragnarsson . 10 pages. AT GR 8 Sep math.AT/0508083

9. Open Problems In Algebraic Topology Problems in algebraic topology, compiled by mathematician Mark Hovey of Wesleyan University. 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)

10. What Is Algebraic Topology? Introductory essay by Joe Neisendorfer, University of Rochester. 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.

11. Algebraic Topology -- From MathWorld Index to more than 100 articles on algebraic topology. http://mathworld.wolfram.com/topics/AlgebraicTopology.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Topology Algebraic Topology Absolute Retract Homologous Retraction Abstract Simplicial Co... ... Retract

12. Algebraic Topology - Wikipedia, The Free Encyclopedia An encyclopedic reference containing definitions, some discussion, and an assortment of useful links to various resources concerning algebraic topology and http://en.wikipedia.org/wiki/Algebraic_topology

Algebraic topology From Wikipedia, the free encyclopedia. Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces Contents The method of algebraic invariants Results on homology Setting in category theory The problems of algebraic topology ... edit 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 constructed from simpler ones. The basic method now applied in algebraic topology is to investigate spaces via algebraic invariants, by mapping them, for example, 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 generally 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)

13. 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

14. Algebraic Topology & Concurrency A collection of preprints on the applications of algebraic topology to Computer Science, such as the use of topological techniques to formulate synchronous http://www.ipipan.gda.pl/~stefan/AlgTop/

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15. Nantes 3-7 Sept 2001 University of Nantes, France; 37 September 2001. http://www.math.sciences.univ-nantes.fr/~franjou/2001.html

http://www.math.sciences.univ-nantes.fr/~franjou/2001.html En francais last modified: July 19, 2001 UMR 6629 G.D.R.E.1110 Algebraic Topology Conference University of Nantes September 3 - 7 , 2001 Deadline for registration: July 6, 2001. Registration is now closed Check your registration: please check that your name appears in the List of registered participants . If you do not appear on the list, although you sent us registration, please re-send the form at NCAT@math.univ-nantes.fr Get updated information http://www.math.sciences.univ-nantes.fr/~franjou/2001pratique.html Scientific program Schedule of talks List of registered participants ... Maps SCIENTIFIC PROGRAM The scientific program concerns main research fields in Modern Homotopy Theory: Algebraic Homotopy Theory, Unstable Modules over the Steenrod algebra, MacLane Homology, Operads, Loop space homology, Cyclic Homology, Algebraic K-theory. Algebraic Topology coming from problems of Geometric Topology, e.g. Knot Theory, Low dimensional Manifolds, Foliations, will also be included. The Program will contain one hour keynote talks by invited speakers, three lectures on Knot Invariants

16. 55 Algebraic Topology Encyclopedic reference for _QUOTATION_algebraic topology_QUOTATION_ in Dave Rusin's Mathematical Atlas. Includes a brief history along with various http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. What Is Topology? We can analyse the structure of Y using the methods of algebraic topology, and learn a number of interesting and nontrivial things about it. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

18. Algebraic Geometric Topology Colin Rourke Brian Sanderson. Algebraic Geometric Topology ISSN 14722739 (on-line) 1472-2747 (printed) Algebraic Geometric Topology http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. Essays About Algebraic Topology Essays about algebraic topology. Survey articles for the general public algebraic topology entry in Wikipedia (online encyclopedia) 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). A brief history of topology by Artur Gorka (Clemson Univ) 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

20. 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

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