Character Variety - Connection To Geometry

Connection To Geometry

There is an interplay between these moduli and the moduli of principal bundles, vector bundles, Higgs bundles, and geometric structures on topological spaces, given generally by the observation that, at least locally, equivalent objects in these categories are parameterized by conjugacy classes of holonomy homomorphisms. In other words, with respect to a base space for the bundles or a fixed topological space for the geometric structures the holonomy homomorphism is a group homomorphism between and the structure group of the base space.