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         Algebraic Topology:     more books (100)
  1. A User's Guide to Algebraic Topology (Mathematics and Its Applications) by C.T. Dodson, P.E. Parker, et all 1997-01-31
  2. Algebraic Topology (EMS Textbooks in Mathematics) by Tammo Tom Dieck, 2008-09-15
  3. Differential Algebraic Topology (Graduate Studies in Mathematics) by Matthias Kreck, 2010-05-04
  4. Essential Topology (Springer Undergraduate Mathematics Series) by Martin D. Crossley, 2005-07-01
  5. Algebraic Topology: A First Course (Mathematics Lecture Note Series) by Marvin J. Greenberg, John R. Harper, 1981-01-22
  6. Algebraic Topology via Differential Geometry (London Mathematical Society Lecture Note Series) by M. Karoubi, C. Leruste, 1988-01-29
  7. Lectures on algebraic topology (Mathematics lecture note series) by Marvin J Greenberg, 1967
  8. Introduction to Differential and Algebraic Topology (Texts in the Mathematical Sciences) by Yu.G. Borisovich, N.M. Bliznyakov, et all 2010-11-02
  9. Algebraic Topology by Robert M. Switzer, 2002-02-26
  10. Quadratic Forms with Applications to Algebraic Geometry and Topology (London Mathematical Society Lecture Note Series) by Albrecht Pfister, 1995-10-27
  11. Foundations of Algebraic Topology (Mathematics Series) by Samuel Eilenberg, Norman E. Steenrod, 1952-12
  12. Homology Theory: An Introduction to Algebraic Topology (Graduate Texts in Mathematics) (v. 145) by James W. Vick, 1994-01-07
  13. Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics) (v. 1) by Claire Voisin, 2008-02-04
  14. A Combinatorial Introduction to Topology by Michael Henle, 1994-03-14

41. Allen Hatcher's Homepage
Links to online texts and papers (published and unpublished) on Algebraic Topology, KTheory, and 3-Manifolds.
Allen Hatcher
Office: 553 Malott Hall
Phone: (607)-255-4091
Book Projects: Course Notes: Papers Other Things: Book Projects
Algebraic Topology
This is the first in a planned 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 second and third books 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 intention 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

42. University Of Chicago Algebraic Topology Seminar
To request a future speaker or for questions, please contact Vigleik Angeltveit (vigleik AT To sign up for electronic announcements of talks, please visit
University of Chicago Algebraic Topology Seminar
Algebraic Topology Seminar
Location: Room 203 in Eckhart Hall Directions
Day: Tuesdays
Time: Pretalk at 3:00, Talk at 4:30 (unless otherwise specified)
Practical Information for speakers
To request a future speaker or for questions, please contact Vigleik Angeltveit (vigleik AT
To sign up for electronic announcements of talks, please visit
Here is a link to the proseminar
Autumn 2010 Seminars
    4:30 pm Tuesday, September 28, 2010 in E203
      Algebraic Topology Duality for Topological Modular Forms
      by Vesna Stojanoska (Northwestern)
      It has been observed that certain localizations of the spectrum of topological modular forms tmf are self-dual (Mahowald-Rezk, Gross-Hopkins). We provide an integral explanation of these results that is internal to the geometry of the (compactified) moduli stack of elliptic curves M, yet is only true in the derived setting. When 2 is inverted, choice of level-2-structure for an elliptic curve provides a geometrically well-behaved cover of M, which allows one to consider tmf as the homotopy fixed points of tmf(2), topological modular forms with level-2-structure, under a natural action by GL_2(Z/2). As a result of Grothendieck-Serre duality, we obtain that tmf(2) is self dual. The vanishing of the associated Tate spectrum then makes tmf itself Anderson self-dual.

    4:30 pm Tuesday, October 5, 2010 in E203

43. PlanetMath: Bibliography For Groupoids And Algebraic Topology
The following are recent sources for several areas in abstract algebra, homological algebra, homotopy groups, homotopy groupoids, algebraic topology and higher dimensional algebra (HDA)
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talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About bibliography for groupoids and algebraic topology (Bibliography) The following are recent sources for several areas in abstract algebra , homological algebra, homotopy groups homotopy groupoids algebraic topology and higher dimensional algebra (HDA).
Algebraic Topology and Groupoids
  • Ronald Brown: Topology and Groupoids , BookSurge LLC (2006). Ronald Brown R, P.J. Higgins, and R. Sivera.: ``Non-Abelian algebraic topology" . http://www. .html ; , Springer: in press (2010). R. Brown and J.-L. Loday: Homotopical excision, and Hurewicz theorems , for n-cubes of spaces, Proc. London Math. Soc., 54:(3), 176-192, (1987). R. Brown and J.-L. Loday: Van Kampen Theorems for
  • 44. Front: Math.AT Algebraic Topology
    An archive of pre-publication papers (preprints) on Algebraic Topology.
    Front for the arXiv Fri, 29 Oct 2010
    math AT search register submit
    ... iFAQ math.AT Algebraic Topology Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 28 Oct arXiv:1010.5635 The Segal conjecture for topological Hochschild homology of complex cobordism. Sverre LunøeNielsen , John Rognes math.AT 28 Oct arXiv:1010.5633 The topological Singer construction. Sverre LunøeNielsen , John Rognes math.AT 27 Oct arXiv:1010.5269 The Mayer-Vietoris Property in Differential Cohomology. James Simons , Dennis Sullivan math.AT math.DG math.QA Cross-listings 29 Oct arXiv:1010.6039 A pull-back procedure of the Gromoll-Meyer construction. Llohann D. Sperança math.DG math.AT math.GT 27 Oct arXiv:1009.0793 Notes on noncommutative algebraic topology. Igor Nikolaev math.OA math.AT Revisions 29 Oct arXiv:1009.3622 The homotopy type of toric arrangements. Luca Moci , Simona Settepanella math.AT math.GT math.RT 29 Oct arXiv:1005.4878 Azumaya Objects in Bicategories. Niles Johnson math.AT math.CT math.RA 28 Oct arXiv:0906.0245

    45. Algebraic Topology For Dummies?
    Algebraic topology for dummies? Science Book Discussion discussion

    46. Open Problems In Algebraic Topology
    Problems in Algebraic Topology, compiled by mathematician Mark Hovey of Wesleyan University.
    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 ( 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:

    47. Algebraic Topology: Definition From
    The study of topological properties of figures using the methods of abstract algebra; includes homotopy theory, homology theory, and cohomology theory.

    48. Algebraic Topology -- From Wolfram MathWorld
    Index to more than 100 articles on Algebraic Topology.
    Applied Mathematics

    Calculus and Analysis

    Discrete Mathematics

    Algebraic Topology Absolute Retract Homeomorphism Group Relative Homotopy Group Abstract Simplicial Co... ... Quillen-Lichtenbaum Co...

    49. Algebraic Topology -- From Wolfram MathWorld
    Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, configuration spaces, etc.) that
    Applied Mathematics

    Calculus and Analysis

    Discrete Mathematics
    ... Derwent
    Algebraic Topology Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces spheres tori circles ... links , configuration spaces, etc.) that remain invariant under both-directions continuous one-to-one homeomorphic ) transformations. The discipline of algebraic topology is popularly known as "rubber-sheet geometry" and can also be viewed as the study of disconnectivities . Algebraic topology has a great deal of mathematical machinery for studying different kinds of hole structures, and it gets the prefix "algebraic" since many hole structures are represented best by algebraic objects like groups and rings Algebraic topology originated with combinatorial topology , but went beyond it probably for the first time in the 1930s when was developed. A technical way of saying this is that algebraic topology is concerned with functors from the topological category of groups and homomorphisms . Here, the

    50. Algebraic Topology, Homotopy Theory -
    Mark Feshbach Professor , Ph.D. 1976 Stanford University algebraic topology . David Frank
    Institute of Technology One Stop Directories Search U of M ...
    Graduate Program
    Algebraic Topology, Homotopy Theory
    math page grad page research page
    • Mark Feshbach
      Professor , Ph.D. 1976 Stanford University
      algebraic topology
    • David Frank
      Associate Professor , Ph.D. 1967 University of California Berkeley
      algebraic topology
    • Donald Kahn
      Professor , Ph.D. 1961 Yale University
      algebraic topology, global analysis
    • Tyler Lawson
      Assistant Professor , Ph.D. 2004, Stanford University
      algebraic topology, K-theory
    • Alexander Voronov
      Professor , Ph.D. 1988, Moscow State University
      math physics, algebra, algebraic geometry, algebraic topology
    • Peter Webb Professor , Ph.D. 1979 Queen Mary College, London representation theory of groups and algebras, algebraic topology, combinatorics, category theory
    Director of Graduate Studies in Mathematics 127 Vincent Hall 206 Church St. S.E. Minneapolis, MN 55455 USA URL The University of Minnesota is an equal opportunity educator and employer.

    51. Algebraic Topology Definition Of Algebraic Topology In The Free Online Encyclope
    algebraic topology. Field of mathematics that uses algebraic structures to study transformations of geometric objects. It uses function s (often called maps in this context) to topology

    52. ALGTOP-L, Algebraic Topology Listserv
    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.
    ALGTOP-L, Algebraic Topology listserv
    This listserv began as a discussion group in July 1995, and was converted to an automated moderated listserv in Sept 2007. To join the listserv or use it, go to The primary functions of this listserv are providing information about topology conferences and jobs, 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. As a service for the nonspecialist, we have an

    53. Algebraic Topology - Cambridge University Press
    For price and ordering options, inspection copy requests, and reading lists please select Europe, Middle East and Africa Americas Asia Australia and New Zealand

    54. Algebraic Topology - Cambridge University Press
    Paperback (ISBN13 9780521795401 ISBN-10 0521795400) There was also a Hardback of this title but it is no longer available; Published April 2002

    55. Algebraic Topology
    Article on Algebraic Topology New! You can click on formulas to copy the LaTeX source to your clipboard. Math Videos

    56. K-theory Preprint Archives
    An extensive archive of pre-publication papers (preprints) on Algebraic K-Theory.

    57. The Math Forum - Math Library - Algebraic Topology
    The Math Forum's Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites relating to
    Browse and Search the Library
    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
  • 58. K-theory Calendar
    A calendar of upcoming and past events (workshops, colloquia, lectures) pertaining to K-Theory and its applications.
    K-theory Calendar
    • To get your K-theory event listed here and/or sent out to the K-theory preprint archives mailing list, send email to Dan Grayson
    Related sites
    The future
    • , November 1 - 5, 2010, K-Theory, C*-Algebras and Index Theory Los Angeles , March 22 - 25, 2011, Conference on K-theory and motives , dedicated to Andrei Suslin's 60th birthday.
    The past
    • Bonn , September 6 - 10, 2010, Geometric aspects of motivic homotopy theory Buenos Aires , July 26-August 6, 2010, NCG School: Topics in Non Commutative Geometry Barcelona , July 12 - 22, 2010, Regulators III St. Petersburg , June 25 - 29, 2010, Algebraic Geometry, Algebraic K-theory, and Motives , dedicated to Andrei Suslin's 60th birthday. Lens , June 14 - 18, 2010, Linear Algebraic Groups and Quadratic Forms: Patching, Involutions and Buildings , May 7 - 8, 2010, Thirteenth NRW Topology Meeting Ottawa , March 26 - 28, 2010, Torsors, Lie algebras and Galois cohomology Columbus , November 7 - 8, 2009, Algebraic Cycles III: a follow-up workshop Mainz , October 29 - 30, 2009, Pfister forms , October 8 - 10, 2009, a conference on Combinatorial structures in algebra and topology Loen, Norway

    59. MIT Mathematics | Algebraic Topology
    Algebraic Topology. The notion of shape is fundamental in mathematics. Geometry concerns the local properties of shape such as curvature, while topology involves largescale
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    • Search Sitemap Contact Us About Us selSection('research');
      • Pure
        Algebraic Topology
        Our department has played a seminal role in this line of research, which has now flowered into a major discipline itself. MIT faculty and instructors have gone on to make connections with still more elaborate and contemporary segments of arithmetic algebraic geometry, and are now in the process of reworking this entire area, creating a deep unification of algebraic geometry and algebraic topology. This work will form the foundation of much research over the next decade, and offers the promise of providing tools useful in algebra as well as in topology. Specifically, our group works in stable and unstable homotopy theory, homotopical group theory, higher category theory, derived algebraic geometry, elliptic cohomology, computational homotopy theory and string topology. Research and Training Group Research and training in Geometry and Topology, from the undergraduate to the postdoctoral level, are supported by an RTG grant from the National Science Foundation. For more information about the various RTG activities, see the RTG website
        Clark Barwick Mark Behrens Haynes Miller Massachusetts Institute of Technology
        Department of Mathematics

    60. An Introduction To Algebraic K-theory
    An incomplete graduate textbook in Algebraic K-Theory, by Charles Weibel. Several chapters are available online.
    ``The K-book: An introduction to algebraic K-theory''
  • Introduction here . (These are .dvi files)
  • Chapter I : Projective Modules and Vector Bundles Here is the corresponding .dvi file
    Last major update March 1997. Minor updates July 2000, Sept. 2004, June 2005, May 2007, November 2008.
      1. Free and stably free modules; p.1
      2. Projective modules; p.6
      3. The Picard group of a ring; p.15
      4. Topological vector bundles and Chern classes; p.26
      5. Algebraic vector bundles; p.38
  • Chapter II : The Grothendieck group K_0 (101 pp.) Here is the corresponding .dvi file
    Last major updates Dec. 2003 (sec.6, 7, 9), July 2004 (sec.2, 7, App.).
    Minor updates Sept. 2004, June 2005 (sec.3), August 2006 (Burnside ring), Jan 2007 (compatibility with Chapter V).
      1. group completion of a monoid; p.1
      2. K_0 of a ring; p.5
      3. K(X) of a topological space; p.17
      Lambda and Adams operations; p.24 5. K_0 of a symmetric monoidal category; p.37 6. K_0 of an abelian category; p.45 7. K_0 of an exact category; p.59
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