One-dimensional actions of Higman's group.

IF 1 3区数学 Q1 MATHEMATICS Discrete Analysis Pub Date : 2019-05-02 DOI:10.19086/DA.11151

C. Rivas, Michele Triestino

引用次数: 1

Abstract

We build a faithful action of Higman's group on the line by homeomorphisms, answering a question of Yves de Cornulier. As a by-product we obtain many quasimorphisms from the Higman group into the reals. We also show that every action by $C^1$-diffeomorphisms of Higman's group on the line or the circle is trivial.

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希格曼群的一维作用。

我们通过同胚建立了Higman群在线上的忠实行动，回答了Yves de Cornulier的一个问题。作为副产品，我们得到了许多从Higman群到实数的拟态射。我们还证明了Higman群的$C^1$-微分同胚在直线或圆上的每一个作用都是平凡的。

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

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.

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