Pseudo-Anosov maps with small stretch factors on punctured surfaces

Yazdi, Mehdi¹

¹Mathematical Institute, University of Oxford, Oxford, United Kingdom

Algebraic and Geometric Topology, Tome 20 (2020) no. 4, pp. 2095-2128

Résumé

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.

Détail

DOI : 10.2140/agt.2020.20.2095

Classification : 37B40, 37E30
Keywords: pseudo-Anosov, entropy, stretch factor, dilatation, punctured surfaces

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