NON-REALIZABILITY OF SOME BIG MAPPING CLASS GROUPS

被引：0

作者：

Chen, Lei ^{[1
]}

He, Yan mary ^{[2
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Univ Oklohoma, Dept Math, Norman, OK 73019 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 152卷 / 10期

关键词：

GLOBAL FIXED-POINTS; NIELSEN REALIZATION; BRAID-GROUPS;

D O I：

10.1090/proc/16860

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we prove that the compactly supported mapping class group of a surface containing a genus 3 subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order 6 symmetries, their mapping class groups have no realization as a subgroup of the homeomorphism group. Examples of such surfaces include the plane minus a Cantor set and the sphere minus a Cantor set.

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页码：4503 / 4514

页数：12

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