Higher spin mapping class groups.

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Higher spin mapping class groups are of central importance in the geometry, topology and dynamical theory of surfaces. For instance, recent work of Calderon--Salter shows that modular monodromies of stratum components of moduli spaces of abelian differentials are example of such spin groups and are of importance in the dynamics of Teichmuller flow. These groups also exhibit some nice combinatorial properties, including finite generation, and have been shown to have close connections with Johnson's foundational work on Torelli groups and associated quadratic forms. The project will investigate higher spin groups deeply and from these diverse points of view.