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

Hadari, Asaf¹

¹ Department of Mathematics, University of Hawaii, Honolulu, HI, United States

Geometry & topology, Tome 24 (2020) no. 4, pp. 1717-1750.

Résumé

Let $\Sigma$ be a compact orientable surface of finite type with at least one boundary component. Let $f\in Mod\left(\Sigma \right)$ 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 ${\tilde{f}}_{\ast }:H_1\left(\tilde{\Sigma },\mathbb{Z}\right)\to H_1\left(\tilde{\Sigma },\mathbb{Z}\right)$ has an eigenvalue off the unit circle.

Détail

DOI : 10.2140/gt.2020.24.1717

Classification : 20C12, 57M05, 57M60
Keywords: low-dimensional topology, mapping class groups, representation theory

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