映射类组动作的刚性

IF 2 1区数学

Geometry & Topology Pub Date : 2018-08-09 DOI:10.2140/GT.2020.24.1211

Kathryn Mann, M. Wolff

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引用次数: 16

摘要

具有一个标记点的曲面的映射类组$\mathrm{Mod}_{g, 1}$可以用$\mathrm{Aut}(\pi_1 \Sigma_g)$的索引2子组来标识。对于一个属$g \geq 2$的曲面，我们证明了$\mathrm{Mod}_{g, 1}$在圆上的任何作用或者是它在$\pi_1 \Sigma_g$的Gromov边界上的自然作用的半共轭，或者是通过一个有限循环群的因子。对于$g \geq 3$，所有有限的动作都是微不足道的。这回答了法布的一个问题。

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Rigidity of mapping class group actions on S1

The mapping class group $\mathrm{Mod}_{g, 1}$ of a surface with one marked point can be identified with an index two subgroup of $\mathrm{Aut}(\pi_1 \Sigma_g)$. For a surface of genus $g \geq 2$, we show that any action of $\mathrm{Mod}_{g, 1}$ on the circle is either semi-conjugate to its natural action on the Gromov boundary of $\pi_1 \Sigma_g$, or factors through a finite cyclic group. For $g \geq 3$, all finite actions are trivial. This answers a question of Farb.

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来源期刊

Geometry & Topology 数学-数学

自引率

5.00%

发文量

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.