Volume 19, issue 6 (2015)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Pseudo-Anosov mapping classes not arising from Penner's construction

Hyunshik Shin and Balázs Strenner

Geometry & Topology 19 (2015) 3645–3656
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/