Homological eigenvalues of lifts of pseudo-Anosov mapping classes to finite covers

Abstract

Let $\Sigma$ be a compact orientable surface of finite type with at least one boundary component. Let $f\in \text{Mod}(\Sigma )$ be a pseudo Anosov mapping class. We prove a conjecture of McMullen by showing that there exists a finite cover $\tilde{\Sigma }\to \Sigma$ and a lift $\tilde{f}$ of $f$ such that $\wt{f}_*: H_1(\wtΣ; \mathbb{Z}) \to H_1(\wtΣ; \mathbb{Z})$ has an eigenvalue off the unit circle.

30 pages

References in corpus (1)

• Every Infinite order mapping class has an infinite order action on the homology of some finite cover

Cited by in corpus (2)

• Simple closed curves, finite covers of surfaces, and power subgroups of Out(F_n)
• Virtual homological spectral radii for automorphisms of surfaces