A crossed homomorphism for groups acting on the circle

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2024-02-05 DOI:10.1142/s1793525324500092

Shuhei Maruyama

引用次数: 0

Abstract

In this paper, we construct a crossed homomorphism by using a group action on the circle and the Poincaré translation number. We relate it to the Euler class of the action in terms of the Hochschild–Serre spectral sequence. As an application, we answer a question of Calegari and Chen, which is on an explicit form of a certain crossed homomorphism on the mapping class group of the sphere minus a Cantor set.

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作用于圆的群的交叉同构

在本文中，我们利用圆上的群作用和波恩卡莱平移数构建了一个交叉同态。我们用霍赫希尔德-塞尔谱序列将其与作用的欧拉类联系起来。作为应用，我们回答了 Calegari 和 Chen 提出的一个问题，即关于球面的映射类群减去一个康托集的某个交叉同构的明确形式。

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

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.