Entropy and affine actions for surface groups

نویسندگان

چکیده

We give a short and independent proof of theorem Danciger Zhang: surface groups with Hitchin linear part cannot act properly on the affine space. The is fundamentally different relies ergodic methods.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Affine Actions on Nilpotent Lie Groups

To any connected and simply connected nilpotent Lie group N , one can associate its group of affine transformations Aff(N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N , via such affine transformations. We succeed in translating the existence question of such a simply transitive affine action to a corresponding question on ...

متن کامل

Entropy and the Variational Principle for Actions of Sofic Groups

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants, and we establish the variational princi...

متن کامل

Maximal Entropy Measures for Piecewise Affine Surface Homeomorphisms

We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability measures maximizing entropy and prove a multiplicative lower bound for the number of periodic points. This is intended as a step towards the understanding of s...

متن کامل

Entropy of Gaussian actions for countable Abelian groups

We prove that if a countable Abelian group A satisfies Thouvenot’s conjecture then for any of its Gaussian actions on a standard Borel space the entropy is either zero or infinity, and moreover, the former case happens iff the spectral measure of the Gaussian action is singular with respect to Haar measure on the dual of A. Introduction. In this note we extend a classical result about the entro...

متن کامل

Entropy for expansive algebraic actions of residually finite groups

We prove a formula for the sofic entropy of expansive principal algebraic actions of residually finite groups, extending recent work of Deninger and Schmidt.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Topology

سال: 2022

ISSN: ['1753-8424', '1753-8416']

DOI: https://doi.org/10.1112/topo.12243