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Homotopy types of Spin c(n) -gauge groups over S4

Homotopy types of Spin c(n) -gauge groups over S4
Homotopy types of Spin c(n) -gauge groups over S4

The gauge group of a principal G-bundle P over a space X is the group of G-equivariant homeomorphisms of P that cover the identity on X. We consider the gauge groups of bundles over S4 with Spin c(n) , the complex spin group, as structure group and show how the study of their homotopy types reduces to that of Spin (n) -gauge groups over S4 . We then advance on what is known by providing a partial classification for Spin (7) - and Spin (8) -gauge groups over S4 .

Gauge groups, Homotopy types, Spin groups
2199-675X
Rea, Simon
4207838a-c493-48c2-aa49-728ec02c1e63
Rea, Simon
4207838a-c493-48c2-aa49-728ec02c1e63

Rea, Simon (2023) Homotopy types of Spin c(n) -gauge groups over S4. European Journal of Mathematics, 9 (3), [48]. (doi:10.1007/s40879-023-00636-x).

Record type: Article

Abstract

The gauge group of a principal G-bundle P over a space X is the group of G-equivariant homeomorphisms of P that cover the identity on X. We consider the gauge groups of bundles over S4 with Spin c(n) , the complex spin group, as structure group and show how the study of their homotopy types reduces to that of Spin (n) -gauge groups over S4 . We then advance on what is known by providing a partial classification for Spin (7) - and Spin (8) -gauge groups over S4 .

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Accepted/In Press date: 25 March 2023
Published date: September 2023
Additional Information: Funding Information: Funding was provided by the Engineering and Physical Sciences Research Council (Grant No. 1985336). Publisher Copyright: © 2023, The Author(s).
Keywords: Gauge groups, Homotopy types, Spin groups

Identifiers

Local EPrints ID: 479011
URI: http://eprints.soton.ac.uk/id/eprint/479011
ISSN: 2199-675X
PURE UUID: 9ca9fd57-b882-4ba0-ac41-30885fb0ac49
ORCID for Simon Rea: ORCID iD orcid.org/0000-0002-6822-0523

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Date deposited: 17 Jul 2023 16:57
Last modified: 05 Jun 2024 19:48

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Author: Simon Rea ORCID iD

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