Non-realizability of some big mapping class groups

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-03-29 DOI:10.1090/proc/16860

Lei Chen, Yan Mary He

引用次数: 0

Abstract

In this note, we prove that the compactly supported mapping class group of a surface containing a genus 3 3 subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order 6 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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某些大型映射类群的不可实现性

在本注释中，我们证明了包含属 3 3 子曲面的曲面的紧凑支撑映射类群没有实现为同构群的子群。我们还证明，对于某些具有 6 6 阶对称性的曲面，它们的映射类群没有实现为同构群的子群。这类曲面的例子包括平面减去一个康托集和球面减去一个康托集。

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

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.