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
Rea, Simon
4207838a-c493-48c2-aa49-728ec02c1e63
September 2023
Rea, Simon
4207838a-c493-48c2-aa49-728ec02c1e63
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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s40879-023-00636-x
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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
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Date deposited: 17 Jul 2023 16:57
Last modified: 17 Mar 2024 13:24
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Author:
Simon Rea
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