Pseudo-Anosov maps with small stretch factors on punctured surfaces

Yazdi, Mehdi

doi:10.2140/agt.2020.20.2095

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Pseudo-Anosov maps with small stretch factors on punctured surfaces

Mehdi Yazdi

Algebraic & Geometric Topology 20 (2020) 2095–2128

DOI: 10.2140/agt.2020.20.2095

Abstract

Consider the problem of estimating the minimum entropy of pseudo-Anosov maps on a surface of genus $g$ with $n$ punctures. We determine the behavior of this minimum number for a certain large subset of the $(g, n)$ plane, up to a multiplicative constant. In particular, we show that for fixed $n$ , this minimum value behaves as $\frac{1}{g}$ , proving what Penner speculated in 1991.

Keywords

pseudo-Anosov, entropy, stretch factor, dilatation, punctured surfaces

Mathematical Subject Classification 2010

Primary: 37B40, 37E30

References

Publication

Received: 30 April 2019

Revised: 2 October 2019

Accepted: 16 October 2019

Published: 20 July 2020

Authors

Mehdi Yazdi
Mathematical Institute University of Oxford Oxford United Kingdom

Volume 20, issue 4 (2020)