Pseudo-Anosov mapping classes not arising from Penner’s construction

Shin, Hyunshik; Strenner, Balázs

doi:10.2140/gt.2015.19.3645

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Pseudo-Anosov mapping classes not arising from Penner's construction

Hyunshik Shin and Balázs Strenner

Geometry & Topology 19 (2015) 3645–3656

DOI: 10.2140/gt.2015.19.3645

Abstract

We show that Galois conjugates of stretch factors of pseudo-Anosov mapping classes arising from Penner’s construction lie off the unit circle. As a consequence, we show that, for all but a few exceptional surfaces, there are examples of pseudo-Anosov mapping classes so that no power of them arises from Penner’s construction. This resolves a conjecture of Penner.

Keywords

pseudo-Anosov, mapping class group, Penner's construction

Mathematical Subject Classification 2010

Primary: 37E30

Secondary: 57M99, 15A18, 11R32

References

Publication

Received: 11 February 2015

Accepted: 12 March 2015

Published: 6 January 2016

Proposed: Benson Farb

Seconded: Ian Agol, David Gabai

Authors

Hyunshik Shin
Department of Mathematical Sciences KAIST 291 Daehak-ro Yuseong-gu Daejeon 34141 South Korea
http://mathsci.kaist.ac.kr/~hshin
Balázs Strenner
School of Mathematics Institute for Advanced Study Princeton, NJ 08540 USA
http://math.ias.edu/~strenner/

Volume 19, issue 6 (2015)