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.

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)