MOS

Abstract

An Ehresmann structure on a manifold is a geometric structure defined by an atlas of local coordinate charts into a fixed homogeneous space. These structures form deformation spaces which themselves are modeled on the space of representations of the fundamental group. These deformation spaces admit actions of the mapping class group, whose dynamics can be highly nontrivial. In many cases the deformation space embeds inside the space of representations of the fundamental group, and geometric structures provide a powerful tool to study representation spaces of surface groups. This talk will survey several examples of these structures and relate them to other classification problems.