On the nonrealizability of braid groups by homeomorphisms

IF 2 1区数学

Geometry & Topology Pub Date : 2018-08-24 DOI:10.2140/gt.2019.23.3735

Lei Chen

引用次数: 5

Abstract

In this paper, we will show that the projection $\text{Homeo}^+(D^2_n)\to B_n$ does not have a section; i.e. the braid group $B_n$ cannot be geometrically realized as a group of homeomorphisms of a disk fixing the boundary point-wise and $n$ marked points in the interior as a set. We also give a new proof of a result of Markovic that the mapping class group of a closed surface cannot be geometrically realized as a group of homeomorphisms.

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用同胚论辫群的不可实现性

在本文中，我们将证明$\text{Homeo}^+(D^2_n)\到B_n$的投影没有截面;即，编织群$B_n$不能在几何上实现为沿边界点固定的盘的同胚群，内部的$n$标记点为集合。我们还给出了Markovic关于闭曲面的映射类群不能在几何上实现为一组同胚的结果的一个新的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.