We prove the following well known conjecture: let $\Sigma$ be an oriented surface of finite type whose fundamental group is a nonabelian free group. Let $\phi \in \textup{ Mod}(\Sigma)$ be a an infinite order mapping class. Then there exists a finite solvable cover $\widehat{ \Sigma} \to \Sigma$, and a lift $\widehat{ \phi}$ of $\phi$ such that the action of $\widehat{ \phi}$ on $H_1(\widehat{ \Sigma}, \mathbb{ Z})$ has infinite order. Our main tools are the theory of homological shadows, which was previously developed by the author, and Fourier analysis
Categories: math.GT