穿刺表面和体积上的低膨胀伪阿诺索夫。

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2023-12-09 DOI:10.1007/s10711-023-00860-5

Shixuan Li

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引用次数: 0

摘要

对于熵为 \(\frac{1}{g}\)阶（可能的最低阶）的封闭表面上的伪阿诺索夫同构 f，法布-莱宁格-马格利特（Farb-Leininger-Margalit）证明了映射环的体积是有界的，与 g 无关。我们通过构造熵为最小阶 \(\frac\{log n}{n}\)、体积趋于无穷大的伪阿诺索夫同构，证明了对于具有 n 个穿刺点的固定属g曲面，类似的结果是失败的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Low dilatation pseudo-Anosovs on punctured surfaces and volume.

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Low dilatation pseudo-Anosovs on punctured surfaces and volume.

For a pseudo-Anosov homeomorphism f on a closed surface of genus \(g\ge 2\), for which the entropy is on the order \(\frac{1}{g}\) (the lowest possible order), Farb-Leininger-Margalit showed that the volume of the mapping torus is bounded, independent of g. We show that the analogous result fails for a surface of fixed genus g with n punctures, by constructing pseudo-Anosov homeomorphism with entropy of the minimal order \(\frac{\log n}{n}\), and volume tending to infinity.

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.