Original scientific paper

https://doi.org/10.3336/gm.57.2.09

Topological entropy of pseudo-Anosov maps on punctured surfaces vs. homology of mapping tori

Hyungryul Baik ; Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
Juhun Baik orcid.org/0000-0002-4167-2722 ; Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
Changsub Kim ; Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
Philippe Tranchida orcid.org/0000-0003-0744-4934 ; Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea

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Abstract

We investigate the relation between the topological entropy of pseudo-Anosov maps on surfaces with punctures and the rank of the first homology of their mapping tori. On the surface \(S\) of genus \(g\) with \(n\) punctures, we show that the minimal entropy of a pseudo-Anosov map is bounded from above by \(\dfrac{(k+1)\log(k+3)}{|\chi(S)|}\) up to a constant multiple when the rank of the first homology of the mapping torus is \(k+1\) and \(k, g, n\) satisfy a certain assumption. This is a partial generalization of precedent works of Tsai and Agol-Leininger-Margalit.

Keywords

Fibered \(3\)-manifold, homology, pseudo-Anosov map, topological entropy

Hrčak ID:

289611

URI

https://hrcak.srce.hr/289611

Publication date:

30.12.2022.

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