Directory of Algebraic Topology Resources

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Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces.

Resources in This Category

• Algebraic K-theory, Groups and Categories

  http://pages.bangor.ac.uk/~mas010/intasrep.html
  A report pursuant to the amalgamation in 1995 of two separate proposals for INTAS support in the areas of Algebraic K-theory, and Categorical Methods in Algebraic Homotopy and related topics. Period covered: 1997-2000. Project Coordinator: Prof. R. Brown

• Algebraic Topology

  http://en.wikipedia.org/wiki/Algebraic_topology
  An encyclopedic reference containing definitions, some discussion, and an assortment of useful links to various resources concerning Algebraic Topology and K-Theory.

• Algebraic Topology Discussion List

  http://www.lehigh.edu/dmd1/public/www-data/algtop.html
  Includes information on subscribing, archives of past discussions, and links to home pages of algebraic topologists and other related resources.

• Algebraic Topology Textbook

  http://www.math.cornell.edu/~hatcher/AT/ATpage.html
  A complete, downloadable, introductory text on Algebraic Topology, by Prof. Allen Hatcher, Cornell Univ. 3rd Ed. 553 pp. with illustrations. Available in pdf and postscript versions.

• Algorithms for the Fixed Point Property

  http://www.csi.uottawa.ca/ordal/papers/schroder/FINSURVE.html
  A survey of various algorithms used to determine if a given ordered set has the fixed point property, that is, whether it has a fixed point free order-preserving self-map. Algorithms using the methods of Algebraic Topology are compared with other techniques.

• Allen Hatcher's Homepage

  http://www.math.cornell.edu/~hatcher/
  Links to online texts and papers (published and unpublished) on Algebraic Topology, K-Theory, and 3-Manifolds.

• An Introduction to Algebraic K-theory

  http://math.rutgers.edu/~weibel/Kbook.html
  An incomplete graduate textbook in Algebraic K-Theory, by Charles Weibel. Several chapters are available online.

• British Topology Home Page

  http://www.maths.gla.ac.uk/~ajb/btop.phtml
  A usable collection of pointers to Topology-related sites, including archives and conference announcements. The focus is mainly on British and European resources, with some links and references to research conducted in other parts of the globe.

• Ext Charts

  http://www.nullhomotopie.de/charts/
  Charts for modules over the odd-primary Steenrod Algebra, by Christian Nassau. In Postscript.

• Five Talks on the Poincaré Conjecture

  http://www.math.osu.edu/lectures/clemens/five_talks.html
  Streaming video links to lectures by Prof. John Morgan filmed during a 5-day series held at Columbia University in 2003. Thurston Geometrization, and Hamilton’s ‘Ricci flow’ method, leading up to the Perelman’s proposed proof, are discussed. RealOne Player is required to view the video.

• K-theory Calendar

  http://www.math.uiuc.edu/K-theory/Calendar/
  A calendar of upcoming and past events (workshops, colloquia, lectures) pertaining to K-Theory and its applications.

• K-theory Preprint Archives

  http://www.math.uiuc.edu/K-theory/
  An extensive archive of pre-publication papers (preprints) on Algebraic K-Theory.

• Math Front: AT Algebraic Topology

  http://front.math.ucdavis.edu/math.AT
  An archive of pre-publication papers (preprints) on Algebraic Topology.

• MathWorld

  http://mathworld.wolfram.com/topics/AlgebraicTopology.html
  Index to more than 100 articles on Algebraic Topology.

• Poincaré Conjecture -- from MathWorld

  http://mathworld.wolfram.com/PoincareConjecture.html
  A widely accessible statement of the Poincaré Conjecture and its implications, with various links and references for further inquiry.

• Surgery Bits and Pieces

  http://www.maths.ed.ac.uk/~aar/surgery/index.htm
  Assorted articles and minutia concerning Algebraic Surgery, assembled by Andrew Ranicki.

• Table of the Homotopy Groups of Spheres

  http://www.math.nus.edu.sg/~matwujie/homotopy_groups_sphere.html
  From Toda's book: "Composition Methods in Homotopy Groups of Spheres."

• What is Algebraic Topology?

  http://www.math.rochester.edu/people/faculty/jnei/algtop.html
  Introductory essay by Joe Neisendorfer, University of Rochester.

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