Algebraic entropy and the action of mapping class groups on character varieties

作者：Hadari Asaf^*

来源：Advances in Mathematics, 2011, 226(4): 3282-3296.

DOI：10.1016/j.aim.2010.10.013

• Mapping class group
• Character variety
• Algebraic entropy

We extend the definition of algebraic entropy to endomorphisms of affine varieties. We then calculate the 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.

• 出版日期2011-3-1