Research

Linear representations of the mapping class group of dimension at most 3g − 3

with Julian Kaufmann, Nick Salter, Xiyan Zhong arxiv pdf

Abstract: We classify representations of the mapping class group of a surface of genus g (with at most one puncture or boundary component) up to dimension 3g − 3. Any such representation is the direct sum of a representation in dimension 2g or 2g + 1 (given as the action on the (co)homology of the surface or its unit tangent bundle) with a trivial representation. As a corollary, any linear system on the moduli space of Riemann surfaces of genus g in this range is of algebro-geometric origin.