Homotopy decompositions of the classifying spaces of pointed gauge groups
Homotopy decompositions of the classifying spaces of pointed gauge groups
Let G be a topological group and let G∗(P) be the pointed gauge group of a principal G-bundle P → M. We prove that if G is homotopy commutative then the homotopy type of the classifying space BG∗(P) can be completely determined for certain M. This also works p-locally, and valid choices of M include closed simply-connected four-manifolds when localized at an odd prime p. In this case, an application is to calculate part of the mod-p homology of the classifying space of the full gauge group.
gauge group, mapping space, homotopy type, homology
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Theriault, Stephen
(2019)
Homotopy decompositions of the classifying spaces of pointed gauge groups.
Pacific Journal of Mathematics, 300 (1).
(doi:10.2140/pjm.2019.300.215).
Abstract
Let G be a topological group and let G∗(P) be the pointed gauge group of a principal G-bundle P → M. We prove that if G is homotopy commutative then the homotopy type of the classifying space BG∗(P) can be completely determined for certain M. This also works p-locally, and valid choices of M include closed simply-connected four-manifolds when localized at an odd prime p. In this case, an application is to calculate part of the mod-p homology of the classifying space of the full gauge group.
Text
Bgauge_decomp_revised2
- Accepted Manuscript
More information
Accepted/In Press date: 10 August 2018
e-pub ahead of print date: 20 July 2019
Keywords:
gauge group, mapping space, homotopy type, homology
Identifiers
Local EPrints ID: 424252
URI: http://eprints.soton.ac.uk/id/eprint/424252
ISSN: 0030-8730
PURE UUID: 7bb3faef-20b5-4ac9-a9cd-c11929043db7
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Date deposited: 05 Oct 2018 11:35
Last modified: 06 Jun 2024 04:12
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