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Homotopy decompositions of P U (n) -gauge groups over Riemann surfaces

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
0129-167X
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
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).

Record type: Article

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.

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PUpgauge revised 2 - Accepted Manuscript
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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
ORCID for Stephen Theriault: ORCID iD orcid.org/0000-0002-7729-5527

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Date deposited: 07 Feb 2022 17:42
Last modified: 06 Jun 2024 04:18

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