紧阿贝尔李群表示空间上的模轨道

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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