Algebraic Entropy and the Action of Mapping Class Groups on Character\n Varieties

2008/12/03 by Asaf Hadari, Hadari, Asaf
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0812.0853

openalex publication_date 2008/12/03 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We extend the definition of algebraic entropy to endomorphisms of affine\nvarieties. We calculate algebraic entropy of the action of elements of mapping\nclass groups on various character varieties, and show that it is equal to a\nquantity we call the spectral radius, a generalization of the dilatation of a\nPseudo-Anosov mapping class. Our calculations are compatible with all known\ncalculations of the topological entropy of this action.\n

Related

• Entropy on abelian groups
• Topological Entropy and Algebraic Entropy for group endomorphisms
• Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups
• Algebraic Yuzvinski Formula
• Algebraic entropy for smooth projective varieties