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

Hadari, Asaf

doi:10.2140/gt.2020.24.1717

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

Asaf Hadari

Geometry & Topology 24 (2020) 1717–1750

DOI: 10.2140/gt.2020.24.1717

Abstract

Let $Σ$ be a compact orientable surface of finite type with at least one boundary component. Let $f \in Mod (Σ)$ be a pseudo-Anosov mapping class. We prove a conjecture of McMullen by showing that there exists a finite cover $\tilde{Σ} \to Σ$ and a lift $\tilde{f}$ of $f$ such that ${\tilde{f}}_{*} : H_{1} (\tilde{Σ}, ℤ) \to H_{1} (\tilde{Σ}, ℤ)$ has an eigenvalue off the unit circle.

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Keywords

low-dimensional topology, mapping class groups, representation theory

Mathematical Subject Classification 2010

Primary: 20C12, 57M05, 57M60

References

Publication

Received: 11 December 2017

Revised: 25 September 2019

Accepted: 2 October 2019

Published: 10 November 2020

Proposed: Étienne Ghys

Seconded: Martin Bridson, Benson Farb

Authors

Asaf Hadari
Department of Mathematics University of Hawaii Honolulu, HI United States

Volume 24, issue 4 (2020)