Algebraic & Geometric Topology

Algebraic degrees of stretch factors in mapping class groups

Hyunshik Shin

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We explicitly construct pseudo-Anosov maps on the closed surface of genus g with orientable foliations whose stretch factor λ is a Salem number with algebraic degree 2g. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree d, for each positive even integer d such that  d g.

Article information

Algebr. Geom. Topol., Volume 16, Number 3 (2016), 1567-1584.

Received: 25 September 2014
Revised: 16 September 2015
Accepted: 21 September 2015
First available in Project Euclid: 28 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds 57M15: Relations with graph theory [See also 05Cxx]

pseudo-Anosov stretch factor dilatation algebraic degree Salem number


Shin, Hyunshik. Algebraic degrees of stretch factors in mapping class groups. Algebr. Geom. Topol. 16 (2016), no. 3, 1567--1584. doi:10.2140/agt.2016.16.1567.

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