Equivariant higher twisted K-theory of SU(n) for exponential functor twists

Evans, David E. and Pennig, Ulrich ORCID: https://orcid.org/0000-0001-5441-6130 2022. Equivariant higher twisted K-theory of SU(n) for exponential functor twists. Journal of Topology 15 (2) , pp. 896-949. 10.1112/topo.12219

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Abstract

We prove that each exponential functor on the category of finite-dimensional complex inner product spaces and isomorphisms gives rise to an equivariant higher (that is, non-classical) twist of K-theory over G=SU(n). This twist is represented by a Fell bundle E→G, which reduces to the basic gerbe for the top exterior power functor. The groupoid G comes equipped with a G-action and an augmentation map G→G, that is an equivariant equivalence. The C∗-algebra C∗(E) associated to E is stably isomorphic to the section algebra of a locally trivial bundle with stabilised strongly self-absorbing fibres. Using a version of the Mayer–Vietoris spectral sequence, we compute the equivariant higher twisted K-groups KG∗(C∗(E)) for arbitrary exponential functor twists over SU(2), and also over SU(3) after rationalisation.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	London Mathematical Society
ISSN:	1753-8416
Funders:	EPSRC
Date of First Compliant Deposit:	21 December 2021
Date of Acceptance:	20 December 2021
Last Modified:	04 Jul 2024 08:44
URI:	https://orca.cardiff.ac.uk/id/eprint/146275

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