Applications of the algebraic geometry of the Putman–Wieland conjecture

Abstract

AbstractWe give two applications of our prior work toward the Putman–Wieland conjecture. First, we deduce a strengthening of a result of Marković–Tošić on virtual mapping class group actions on the homology of covers. Second, let and let be a finite ‐cover of topological surfaces. We show the virtual action of the mapping class group of on an ‐isotypic component of has nonunitary image.