Commensurated hyperbolic subgroups

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-05-11 DOI:10.1090/tran/9209

Nir Lazarovich, Alex Margolis, Mahan Mj

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引用次数: 0

Abstract

We show that if H H is a non-elementary hyperbolic commensurated subgroup of infinite index in a hyperbolic group G G , then H H is virtually a free product of hyperbolic surface groups and free groups. We prove that whenever a one-ended hyperbolic group H H is a fiber of a non-trivial hyperbolic bundle then H H virtually splits over a 2-ended subgroup.

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共轭双曲子群

我们证明，如果 H H 是双曲群 G G 中一个无穷索引的非元素双曲共轭子群，那么 H H 实际上是双曲曲面群和自由群的自由积。我们证明，只要单端双曲群 H H 是非三端双曲束的纤维，那么 H H 实际上就分裂于一个二端子群之上。

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

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 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 research articles in all areas of pure and applied mathematics. To be published in the Transactions, 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. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.