Algebraic degrees of stretch factors in mapping class groups

Shin, Hyunshik

doi:10.2140/agt.2016.16.1567

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Algebraic degrees of stretch factors in mapping class groups

Hyunshik Shin

Algebraic & Geometric Topology 16 (2016) 1567–1584

DOI: 10.2140/agt.2016.16.1567

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 $2 g$ . 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 $d \leq g$ .

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

Volume 16, issue 3 (2016)