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Homotopy theory of gauge groups over 4-manifolds

Homotopy theory of gauge groups over 4-manifolds
Homotopy theory of gauge groups over 4-manifolds
Given a principal G-bundle P over a space X, the gauge group G(P) of P is the topological group of G-equivariant automorphisms of P which fix X. The study of gauge groups has a deep connection to topics in algebraic geometry and the topology of 4-manifolds. Topologists have been studying the topology of gauge groups of principal G-bundles over 4-manifolds for a long time. In this thesis, we investigate the homotopy types of gauge groups when X is an orientable, connected, closed 4-manifold. In particular, we study the homotopy types of gauge groups when X is a non-simply-connected 4-manifold or a simply-connected non-spin 4-manifold. Furthermore, we calculate the orders of the Samelson products on low rank Lie groups, which help determine the classification of gauge groups over S4.
University of Southampton
So, Tse Leung
175505d4-3a13-4bb3-8f99-f24502cfcc2d
So, Tse Leung
175505d4-3a13-4bb3-8f99-f24502cfcc2d
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80

So, Tse Leung (2018) Homotopy theory of gauge groups over 4-manifolds. University of Southampton, Doctoral Thesis, 117pp.

Record type: Thesis (Doctoral)

Abstract

Given a principal G-bundle P over a space X, the gauge group G(P) of P is the topological group of G-equivariant automorphisms of P which fix X. The study of gauge groups has a deep connection to topics in algebraic geometry and the topology of 4-manifolds. Topologists have been studying the topology of gauge groups of principal G-bundles over 4-manifolds for a long time. In this thesis, we investigate the homotopy types of gauge groups when X is an orientable, connected, closed 4-manifold. In particular, we study the homotopy types of gauge groups when X is a non-simply-connected 4-manifold or a simply-connected non-spin 4-manifold. Furthermore, we calculate the orders of the Samelson products on low rank Lie groups, which help determine the classification of gauge groups over S4.

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Published date: July 2018

Identifiers

Local EPrints ID: 428056
URI: https://eprints.soton.ac.uk/id/eprint/428056
PURE UUID: c9667dcc-2a0d-48af-95f7-001c5964d06f
ORCID for Stephen Theriault: ORCID iD orcid.org/0000-0002-7729-5527

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Date deposited: 07 Feb 2019 17:30
Last modified: 14 Mar 2019 01:35

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