Glasnik Matematicki, Vol. 57, No. 2 (2022), 291-312. \( \)

TOPOLOGICAL ENTROPY OF PSEUDO-ANOSOV MAPS ON PUNCTURED SURFACES VS. HOMOLOGY OF MAPPING TORI

Hyungryul Baik, Juhun Baik, Changsub Kim and Philippe Tranchida

Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
e-mail:hrbaik@kaist.ac.kr

Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
e-mail:jhbaik@kaist.ac.kr

Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
e-mail:kcs55505@kaist.ac.kr

Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
e-mail:tranchida.philippe@gmail.com

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.

2020 Mathematics Subject Classification.   37E30, 57M99

Key words and phrases.   Fibered \(3\)-manifold, homology, pseudo-Anosov map, topological entropy

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

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