Normalized entropy versus volume for pseudo-Anosovs

Sadayoshi Kojima, Greg McShane

研究成果: Article

4 引用 (Scopus)

抜粋

Thanks to a recent result by Jean-Marc Schlenker, we establish an explicit linear inequality between the normalized entropies of pseudo-Anosov automorphisms and the hyperbolic volumes of their mapping tori. As corollaries, we give an improved lower bound for values of entropies of pseudo-Anosovs on a surface with fixed topology, and a proof of a slightly weaker version of the result by Farb, Leininger and Margalit first, and by Agol later, on finiteness of cusped manifolds generating surface automorphisms with small normalized entropies. Also, we present an analogous linear inequality between the Weil-Petersson translation distance of a pseudo-Anosov map (normalized by multiplying by the square root of the area of a surface) and the volume of its mapping torus, which leads to a better bound.

元の言語English
ページ(範囲)2403-2426
ページ数24
ジャーナルGeometry and Topology
22
発行部数4
DOI
出版物ステータスPublished - 2018 4 5
外部発表Yes

ASJC Scopus subject areas

  • Geometry and Topology

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