Commutative Complex K-theory Seminar: Simon Gritschacher

Last time we have seen that the spectrum for commutative K-theory is equivalent to the ku-group ring of BU(1). In this second talk I will show how this induces a splitting of the space BcomU as a product of all the stages in the Whitehead tower for BU. I will then explain the relationship between the homotopy groups of BcomU and certain rational characteristic classes introduced by Adem and Gomez. Finally, I would like to explain an alternative but equivalent picture using Segal's Dold-Thom functor for K-homology theory.