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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Rational algebraic $K$–theory of topological $K$–theory

Christian Ausoni and John Rognes

Geometry & Topology 16 (2012) 2037–2065
Abstract

We show that after rationalization there is a homotopy fiber sequence

BBU K(ku) K().

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 X. We also rationally compute K(KU) by using the localization sequence, and K(MU) by a method that applies to all connective S–algebras.

Keywords
algebraic $K$–theory, rational homotopy, topological $K$–theory, bordism spectra, determinants
Mathematical Subject Classification 2000
Primary: 55N15
Secondary: 18F25, 19Lxx
References
Publication
Received: 10 June 2009
Accepted: 4 April 2012
Published: 3 September 2012
Proposed: John W Morgan
Seconded: Haynes Miller, Peter Teichner
Authors
Christian Ausoni
LAGA
Université Paris 13
Sorbonne Paris Cité
F-93430
Villetaneuse
France
http://www.math.univ-paris13.fr/~ausoni/
John Rognes
Department of Mathematics
University of Oslo
Box 1053 Blindern
0316 Oslo
Norway
http://folk.uio.no/rognes/home.html