Topological entropy of pseudo-Anosov maps on punctured surfaces vs. homology of mapping tori-Reference-Cited by-同舟云学术

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

Published:2022-12-30 Issue:2 Volume:57 Page:291-312
ISSN:0017-095X
Container-title:Glasnik Matematicki
language:
Short-container-title:Glas. Mat. Ser. III

Author:

Baik Hyungryul, ,Baik Juhun,Kim Changsub,Tranchida Philippe, , ,

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.

Publisher

University of Zagreb, Faculty of Science, Department of Mathematics

Subject

General Mathematics

Reference23 articles.

1. I. Agol, C. J. Leininger and D. Margalit, Pseudo-Anosov stretch factors and homology of mapping tori, J. Lond. Math. Soc. (2) 93 (2016), 664-682.

2. H. Baik, E. Kin, H. Shin and C. Wu, Asymptotic translation lengths and normal generation for pseudo-Anosov monodromies of fibered 3-manifolds, arXiv preprint arXiv:1909.00974, 2019.

3. D. Cooper, S. Tillmann, and W. Worden. The Thurston norm via spun-normal immersions, arXiv preprint arXiv:2109.04498, 2021.

4. J. Ellenberg, Pseudo-Anosov puzzle 2: homology rank and dilatation, quomodocumque, 2010.

5. B. Farb, C. J. Leininger and D. Margalit, The lower central series and pseudo-Anosov dilatations, Amer. J. Math. 130 (2008), 799-827.