Groups acting on hyperbolic Λ-metric spaces

Author:

Grecianu Andrei-Paul1,Kvaschuk Alexei V.2,Myasnikov Alexei G.1,Serbin Denis E.1

Affiliation:

1. Stevens Institute of Technology, Department of Mathematical Sciences, 1 Castle Point on Hudson, Hoboken, New Jersey 07030, USA

2. Bank of America Corporate Center, 100 N Tryon St, Charlotte, North Carolina 28255, USA

Abstract

In this paper we study group actions on hyperbolic Λ-metric spaces, where Λ is an ordered abelian group. Λ-metric spaces were first introduced by Morgan and Shalen in their study of hyperbolic structures and then Chiswell, following Gromov's ideas, introduced the notion of hyperbolicity for such spaces. Only the case of 0-hyperbolic Λ-metric spaces (that is, Λ-trees) was systematically studied, while the theory of general hyperbolic Λ-metric spaces was not developed at all. Hence, one of the goals of the present paper was to fill this gap and translate basic notions and results from the theory of group actions on hyperbolic (in the usual sense) spaces to the case of Λ-metric spaces for an arbitrary Λ. The other goal was to show some principal difficulties which arise in this generalization and the ways to deal with them.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Hierarchy for groups acting on hyperbolic ℤn-spaces;International Journal of Algebra and Computation;2021-11-06

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