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

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.

PDF Access Denied

We have not been able to recognize your IP address 44.200.117.166 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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)

Asaf Hadari

Abstract