循环群双曲的相对双曲性

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2020-06-12 DOI:10.4171/ggd/703

Franccois Dahmani, S SurajKrishnaM

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引用次数: 4

摘要

设$G$是无扭双曲群，$\alpha$是$G$的自同构。我们证明了在$\alpha$下存在多项式增长的子群的正则集合，并且$G$乘$\alph$的映射环面相对于$\alpa$下的最大多项式增长子群的暂停是双曲的。

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Relative hyperbolicity of hyperbolic-by-cyclic groups

Let $G$ be a torsion-free hyperbolic group and $\alpha$ an automorphism of $G$. We show that there exists a canonical collection of subgroups that are polynomially growing under $\alpha$, and that the mapping torus of $G$ by $\alpha$ is hyperbolic relative to the suspensions of the maximal polynomially growing subgroups under $\alpha$.

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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.