Volume 24, issue 4 (2020)

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

Asaf Hadari

Geometry & Topology 24 (2020) 1717–1750

Let Σ be a compact orientable surface of finite type with at least one boundary component. Let f Mod(Σ) be a pseudo-Anosov mapping class. We prove a conjecture of McMullen by showing that there exists a finite cover Σ̃ Σ and a lift f̃ of f such that f̃: H1(Σ̃, ) H1(Σ̃, ) has an eigenvalue off the unit circle.

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low-dimensional topology, mapping class groups, representation theory
Mathematical Subject Classification 2010
Primary: 20C12, 57M05, 57M60
Received: 11 December 2017
Revised: 25 September 2019
Accepted: 2 October 2019
Published: 10 November 2020
Proposed: Étienne Ghys
Seconded: Martin Bridson, Benson Farb
Asaf Hadari
Department of Mathematics
University of Hawaii
Honolulu, HI
United States