A well-known conjecture of Ivanov states that mapping class groups of surfaces with genus at least 3 virtually do not surject onto the integers. Putman and Wieland reformulated this conjecture in terms of higher Prym representations of finite-index subgroups of mapping class groups. We show that the Putman-Wieland conjecture holds for geometrically uniform subgroups. Along the way we construct a cover S of the genus 2 surface such that the lifts of simple closed curves do not generate the rational homology of S. This is joint work with Markovic.
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- Junior Topology and Group Theory Seminar