The AH conjecture for Cantor minimal dihedral systems

IF 0.3 4区数学 Q4 MATHEMATICS

Mathematica Scandinavica Pub Date : 2022-06-22 DOI:10.7146/math.scand.a-136741

Eduardo Scarparo

引用次数: 2

Abstract

The AH conjecture relates the low-dimensional homology groups of a groupoid with the abelianization of its topological full group. We show that transformation groupoids of minimal actions of the infinite dihedral group on the Cantor set satisfy this conjecture. The proof uses Kakutani–Rokhlin partitions adapted to such systems.

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Cantor最小二面体系统的AH猜想

AH猜想将群胚的低维同调群与其拓扑全群的交换联系起来。我们证明了Cantor集上无穷二面体群的极小作用的变换群胚满足这个猜想。证明使用了适用于此类系统的Kakutani–Rokhlin分区。

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

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.