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

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

2008-12-04

arxiv.org/abs/0812.0853v2

Mathematics

Dynamical Systems

14 pages

Scientific paper

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

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