Homeomorphisms of 3-manifolds and topological entropy (Q1078857)

The topological entropy of a self-map of a metric space is a measure of its dynamical complexity. The author proves that every homeomorphism of a surface is isotopic to one which realizes the minimum of the topological entropy in its homotopy class. The argument is based on Thurston's canonical form for homeomorphisms of surfaces. Using the case of surfaces, he then proves the same property for a certain class of Seifert 3-manifolds, namely the ones which admit one of Thurston's geometries \(H^ 2\times R\), \(SL_ 2(R)\) or Nil.