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

TL;DR

This paper introduces a simplified method using the Segal spectral sequence to compute twisted K-theory and K-homology of compact simple Lie groups, especially of rank 2, improving upon previous approaches.

Contribution

A new, simpler computational method based on the Segal spectral sequence for twisted K-theory of compact Lie groups, with clarified exposition and corrections.

Findings

Simpler computation method for twisted K-theory of rank 2 Lie groups

Clarified exposition and corrected previous errors

Updated references and improved clarity

Abstract

This paper explores further 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. The exposition has been clarified and one mistake in the previous version has been fixed. Also the references have been updated.