Finiteness of Dirichlet domains of cusped hyperbolic manifolds

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-03-19 DOI:10.1016/j.topol.2025.109349

Hirotaka Akiyoshi

引用次数: 0

Abstract

A Dirichlet domain is a fundamental domain of a hyperbolic manifold associated to a basepoint. We will prove that there appears only finitely many homotopy classes of Dirichlet domains when the basepoint moves around a hyperbolic manifold of finite volume. It is also proved as a corollary that the number of isotopy classes of Dirichlet domains is finite for manifolds of dimension 2 or 3.

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顶角双曲流形的Dirichlet域的有限性

狄利克雷定义域是与基点相关联的双曲流形的基本定义域。我们将证明当基点绕有限体积的双曲流形运动时，狄利克雷域的同伦类只有有限个。并证明了对于2维或3维流形，狄利克雷域的同位素类数是有限的。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.