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.