Volume 16, issue 3 (2016)

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Algebraic degrees of stretch factors in mapping class groups

Hyunshik Shin

Algebraic & Geometric Topology 16 (2016) 1567–1584
Abstract

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.

Keywords
pseudo-Anosov, stretch factor, dilatation, algebraic degree, Salem number
Mathematical Subject Classification 2010
Primary: 57M50, 57M15
References
Publication
Received: 25 September 2014
Revised: 16 September 2015
Accepted: 21 September 2015
Published: 1 July 2016
Authors
Hyunshik Shin
Department of Mathematical Sciences
KAIST
291 Daehak-ro
Yuseong-gu
Daejeon 34141
South Korea
http://mathsci.kaist.ac.kr/~hshin