Representations of Galois Groups on the Homology of Surfaces

Thomas Koberda, Aaron Michael Silberstein

Let $p:{\Sigma }^{\prime }\to \Sigma$ be a finite Galois cover, possibly branched, with Galois group $G$. We are interested in the structure of the cohomology of ${\Sigma }^{\prime }$ as a module over $G$. We treat the c…