Homotopy theory of gauge groups over 4-manifolds

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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ORCID for Stephen Theriault: orcid.org/0000-0002-7729-5527

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