The topology of gauge groups and current groups for 3-manifolds

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Gauge groups and current groups are important in mathematical physics, with gauge groups having important applications in geometry and current groups having important applications in integrable systems. Their topology is concerned with properties that remain unchanged when continuously deformed. In both cases, the group can be described via mapping spaces, which are better suited to analysis using methods from algebraic topology. The mapping spaces involve a base space X and a Lie group G. A great deal of recent work has been done investigating the topology of gauge groups when X is a surface or a four-manifold, but not a 3-manifold. Little has been done to investigate the topology of current groups. This project aims to determine important properties of each in the context of 3-manifolds, properties including their homology and homotopy groups.