Stable algebraic topology 1945-1966, by J.P. May

This is a reasonably comprehensive treatment of the history of stable algebraic topology during the cited period. The table of contents gives an idea of the scope and limitations of the study. The emphasis is on the evolution of ideas, but some mathematical exposition of most of the main results is given. This paper will appear in a volume on the history of topology that is being edited by Ioan James.

Contents:

  • Setting up the foundations
  • The Eilenberg-Steenrod axioms
  • Stable and unstable homotopy groups
  • Spectral sequences and calculations in homology and homotopy
  • Steenrod operations, K(\pi ,n)'s, and characteristic classes
  • The introduction of cobordism
  • The route from cobordism towards K-theory
  • Bott periodicity and K-theory
  • The Adams spectral sequence and Hopf invariant one
  • S-duality and the introduction of spectra
  • Oriented cobordism and complex cobordism
  • K-theory, cohomology, and characteristic classes
  • Generalized homology and cohomology theories
  • Vector fields on spheres and J(X)
  • Further applications and refinements of K-theory
  • Bordism and cobordism theories
  • Further work on cobordism and its relation to K-theory
  • High dimensional geometric topology
  • Iterated loop space theory
  • Algebraic K-theory and homotopical algebra
  • The stable homotopy category
    • The Bibliography lists over 300 items.

    J.P. May <may@math.uchicago.edu>