H-Spaces and Loop Spaces with finiteness conditions
by
Carlos Broto
Universidad Autónoma de Barcelona

A brief historical sketch leads us to the concepts of H-spaces, loop spaces, and, more recently, P-compact groups, introduced by Dwyer-Wilkerson. The techniques used are (for a fixed prime p), p-localization, and p-completion due to Bousfield-Kan, as well as the study of certain functional complexes due to H. Miller (used in the solution of the Sullivan Conjecture) and J. Lannes. Thus we arrive to the homotopy theory of compact Lie groups.

We set in this context our study on loop spaces whose cohomology ring with coefficients in the field with p elements is finitely generated; arriving to the structure theorems due to Crespo and Crespo-Saumell which state that these spaces are essentially p-compact groups, \CC P^\infty, classifying spaces B\ZZ / p^k, and certain extensions of the latter. In particular, we answer a question of Lin ([J. P. Lin, H-spaces with finiteness conditions, Handbook of Algebraic Topology, Ed. I. M. James, Elsevier Science BV, Amsterdam (1995), pgs.1097-1141], Question 2.4)

Date received: March 17, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caak-06.