Rational algebraic K–theory of topological K–theory

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 $ℒ X$ . We also rationally compute $K (K U)$ by using the localization sequence, and $K (M U)$ 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

Volume 16, issue 4 (2012)

Christian Ausoni and John Rognes

Abstract

Keywords

Mathematical Subject Classification 2000

References

Publication

Authors