On the 2-adic K-localizations of H-spaces

A.K. Bousfield

bous@uic.edu

Department of Mathematics
University of Illinois at Chicago
Chicago, IL 60607


We determine the 2-adic K-localizations for a large class of 
H-spaces and related spaces.  As in the odd-primary case, these
localizations are expressed as fibers of maps between specified 
infinite loop spaces, allowing us to approach the 2-primary 
v1-periodic homotopy groups of our spaces.  The present 
v1-periodic results have been applied very successfully to 
simply-connected compact Lie groups by Davis, using knowledge of
the complex, real, and quaternionic representations of the groups.  
We also functorially determine the united 2-adic K-cohomology 
algebras (including the 2-adic KO-cohomology algebras) for all 
simply-connected compact Lie groups in terms of their representation
theories, and we show the existence of spaces realizing a wide 
class of united 2-adic K-cohomology algebras with specified 
operations.