Combinatorial growth in the modular group

IF 0.6 3区数学 Q3 MATHEMATICS Groups Geometry and Dynamics Pub Date : 2020-08-10 DOI:10.4171/ggd/667

Ara Basmajian, R. Valli

引用次数: 1

Abstract

We consider an exhaustion of the modular orbifold by compact subsurfaces and show that the growth rate, in terms of word length, of the reciprocal geodesics on such subsurfaces (so named low lying reciprocal geodesics) converge to the growth rate of the full set of reciprocal geodesics on the modular orbifold. We derive a similar result for the low lying geodesics and their growth rate convergence to the growth rate of the full set of closed geodesics.

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模群中的组合生长

我们考虑了紧致子曲面对模轨道的耗尽，并证明了在这种子曲面上的倒数测地线（即所谓的低位倒数测地线）的增长率，就字长而言，收敛于模轨道上全套倒数测地线的增长率。对于低位测地线，我们得到了类似的结果，并且它们的增长率收敛于全封闭测地线的增长率。

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

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.

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