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Pseudo-Anosov maps with small stretch factors on punctured surfaces

Mehdi Yazdi

Algebraic & Geometric Topology 20 (2020) 2095–2128

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 1 g, proving what Penner speculated in 1991.

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pseudo-Anosov, entropy, stretch factor, dilatation, punctured surfaces
Mathematical Subject Classification 2010
Primary: 37B40, 37E30
Received: 30 April 2019
Revised: 2 October 2019
Accepted: 16 October 2019
Published: 20 July 2020
Mehdi Yazdi
Mathematical Institute
University of Oxford
United Kingdom