Almost finiteness and homology of certain non-free actions

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2020-07-05 DOI:10.4171/ggd/656

E. Ortega, Eduardo Scarparo

引用次数: 7

Abstract

We show that Cantor minimal $\mathbb{Z}\rtimes\mathbb{Z}_2$-systems and essentially free amenable odometers are almost finite. We also compute the homology groups of Cantor minimal $\mathbb{Z}\rtimes\mathbb{Z}_2$-systems and show that the associated transformation groupoids satisfy the HK conjecture if and only if the action is free.

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某些非自由作用的概有限性与同源性

我们证明了康托极小$\mathbb{Z}\r乘以\mathbb{Z}_2$-系统和本质上自由可服从的里程计几乎是有限的。我们还计算了Cantor极小$\mathbb{Z}\r乘以\mathbb{Z}_2$-系统的同调群，并证明了相关的变换群满足HK猜想当且仅当作用是自由的。

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

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.