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Homotopy types of gauge groups of PU (p) -bundles over spheres

Homotopy types of gauge groups of PU (p) -bundles over spheres
Homotopy types of gauge groups of PU (p) -bundles over spheres

We examine the relation between the gauge groups of SU (n) - and PU (n) -bundles over S2i, with 2 ≤ i≤ n, particularly when n is a prime. As special cases, for PU (5 ) -bundles over S4, we show that there is a rational or p-local equivalence G2,k≃ (p)G2,l for any prime p if, and only if, (120 , k) = (120 , l) , while for PU (3 ) -bundles over S6 there is an integral equivalence G3,k≃ G3,l if, and only if, (120 , k) = (120 , l).

Gauge groups, Homotopy types, Samelson products
2193-8407
61-74
Rea, Simon
4207838a-c493-48c2-aa49-728ec02c1e63
Rea, Simon
4207838a-c493-48c2-aa49-728ec02c1e63

Rea, Simon (2021) Homotopy types of gauge groups of PU (p) -bundles over spheres. Journal of Homotopy and Related Structures, 16 (1), 61-74. (doi:10.1007/s40062-020-00274-0).

Record type: Article

Abstract

We examine the relation between the gauge groups of SU (n) - and PU (n) -bundles over S2i, with 2 ≤ i≤ n, particularly when n is a prime. As special cases, for PU (5 ) -bundles over S4, we show that there is a rational or p-local equivalence G2,k≃ (p)G2,l for any prime p if, and only if, (120 , k) = (120 , l) , while for PU (3 ) -bundles over S6 there is an integral equivalence G3,k≃ G3,l if, and only if, (120 , k) = (120 , l).

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More information

Accepted/In Press date: 8 December 2020
e-pub ahead of print date: 21 January 2021
Published date: March 2021
Additional Information: Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
Keywords: Gauge groups, Homotopy types, Samelson products
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Identifiers

Local EPrints ID: 447408
URI: http://eprints.soton.ac.uk/id/eprint/447408
DOI: doi:10.1007/s40062-020-00274-0
ISSN: 2193-8407
PURE UUID: 349160d3-6002-453a-9feb-969f844a296e
ORCID for Simon Rea: ORCID iD orcid.org/0000-0002-6822-0523

Catalogue record

Date deposited: 10 Mar 2021 17:44
Last modified: 16 Mar 2024 10:58

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Author: Simon Rea ORCID iD

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