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

Jonathan Rosenberg

Algebraic & Geometric Topology 20 (2020) 135–167

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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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
Received: 18 August 2017
Revised: 7 August 2018
Accepted: 5 April 2019
Published: 23 February 2020
Jonathan Rosenberg
Department of Mathematics
University of Maryland
College Park, MD
United States