Title:
Rational algebraic K-theory of topological K-theory.

Authors:
Christian Ausoni and John Rognes.

MSC-class: 19D55; 55N99
arXiv:0708.2160v1 [math.KT]

Christian Ausoni 
Mathematical Institute
University of Bonn
Beringstrasse 1
DE - 53113 Bonn

 ausoni@math.uni-bonn.de


John Rognes
Department of Mathematics
University of Oslo
Box 1053, Blindern
NO - 0316 Oslo

 rognes@math.uio.no


Abstract:
We show that after rationalization there is a homotopy 
fiber sequence BBU -> K(ku) -> K(Z). We interpret this 
as a correspondence between the virtual 2-vector bundles 
over a space X and their associated anomaly bundles over 
the free loop space LX. We also rationally compute K(KU) 
by using the localization sequence, and K(MU) by a method 
that applies to all connective S-algebras.