#### Volume 20, issue 1 (2020)

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

### Jonathan Rosenberg

Algebraic & Geometric Topology 20 (2020) 135–167
##### 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