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Abstract
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Let
be
a compact orientable surface of finite type with at least one boundary component. Let
be a
pseudo-Anosov mapping class. We prove a conjecture of McMullen by showing that there exists
a finite cover
and a lift
of
such
that
has an eigenvalue off the unit circle.
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Keywords
low-dimensional topology, mapping class groups,
representation theory
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Mathematical Subject Classification 2010
Primary: 20C12, 57M05, 57M60
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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
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