Homotopy decompositions of P U (n) -gauge groups over Riemann surfaces
Homotopy decompositions of P U (n) -gauge groups over Riemann surfaces
In this paper, we show that the gauge group of a principal PU(n)-bundle over a compact Riemann surface decomposes up to homotopy as the product of factors, one of which is a corresponding gauge group for S2 and the others are immediately recognizable spaces. Further, when n is a prime p, the gauge group for S2 decomposes as a product of immediately recognizable factors. These gauge groups have strong connections to moduli spaces of stable vector bundles.
Gauge group, homotopy type, projective unitary group, Riemann surface
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
1 March 2022
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Theriault, Stephen
(2022)
Homotopy decompositions of P U (n) -gauge groups over Riemann surfaces.
International Journal of Mathematics, 33 (03), [2250025].
(doi:10.1142/S0129167X22500252).
Abstract
In this paper, we show that the gauge group of a principal PU(n)-bundle over a compact Riemann surface decomposes up to homotopy as the product of factors, one of which is a corresponding gauge group for S2 and the others are immediately recognizable spaces. Further, when n is a prime p, the gauge group for S2 decomposes as a product of immediately recognizable factors. These gauge groups have strong connections to moduli spaces of stable vector bundles.
Text
PUpgauge revised 2
- Accepted Manuscript
More information
Accepted/In Press date: 1 January 2022
e-pub ahead of print date: 21 February 2022
Published date: 1 March 2022
Additional Information:
Publisher Copyright:
© 2022 World Scientific Publishing Company.
Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.
Keywords:
Gauge group, homotopy type, projective unitary group, Riemann surface
Identifiers
Local EPrints ID: 454318
URI: http://eprints.soton.ac.uk/id/eprint/454318
ISSN: 0129-167X
PURE UUID: df84d1f3-4cd9-45a3-a68d-7033771f2dcd
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Date deposited: 07 Feb 2022 17:42
Last modified: 17 Mar 2024 07:03
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