Volume 20, issue 4 (2020)

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Pseudo-Anosov maps with small stretch factors on punctured surfaces

Mehdi Yazdi

Algebraic & Geometric Topology 20 (2020) 2095–2128
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 $\left(g,n\right)$ 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.

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