紧阿贝尔李群表示空间上的模轨道

IF 0.6 3区数学 Q3 MATHEMATICS Groups Geometry and Dynamics Pub Date : 2021-03-27 DOI:10.4171/ggd/716

Yohann Bouilly, Gianluca Faraco

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引用次数: 1

摘要

设$S$是一个$g$大于零的闭曲面。本文研究了映射类群对$\Bbb T^n$-字符变化的拓扑动力学作用，给出了Mod$(S)$-轨道致密的充分必要条件。作为一种应用，这种表征提供了关于非齐次丢芬图近似的克罗内克定理的动态证明。

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Modular orbits on the representation spaces of compact abelian Lie groups

Let $S$ be a closed surface of genus $g$ greater than zero. In the present paper we study the topological-dynamical action of the mapping class group on the $\Bbb T^n$-character variety giving necessary and sufficient conditions for Mod$(S)$-orbits to be dense. As an application, such a characterisation provides a dynamical proof of the Kronecker's Theorem concerning inhomogeneous diophantine approximation.

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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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