A new approach to twisted K–theory of compact Lie groups

Rosenberg, Jonathan

doi:10.2140/agt.2020.20.135

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A new approach to twisted $K$–theory of compact Lie groups

Jonathan Rosenberg

Algebraic & Geometric Topology 20 (2020) 135–167

DOI: 10.2140/agt.2020.20.135

Abstract

We further explore the computation of the twisted $K$ –theory and $K$ –homology of compact simple Lie groups, previously studied by Hopkins, Moore, Maldacena–Moore–Seiberg, Braun and Douglas, with a focus on groups of rank $2$ . We give a new method of computation based on the Segal spectral sequence, which seems to us appreciably simpler than the methods used previously, at least in many key cases.

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Keywords

compact Lie group, twisted K–theory, D–brane, WZW model, Segal spectral sequence, Adams–Novikov spectral sequence, Hurewicz map

Mathematical Subject Classification 2010

Primary: 19L50

Secondary: 55R20, 55T15, 57T10, 81T30

References

Publication

Received: 18 August 2017

Revised: 7 August 2018

Accepted: 5 April 2019

Published: 23 February 2020

Authors

Jonathan Rosenberg
Department of Mathematics University of Maryland College Park, MD United States

Volume 20, issue 1 (2020)