A characterization of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant
Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
We show that an orientable pseudo-Anosov map has vanishing Sah-Arnoux-Fathi (SAF) invariant if and only if the minimal polynomial of its dilation is not a reciprocal polynomial. The proof relies on results of Arnoux, Kenyon-Smillie, and Calta-Smillie. We also show that every bi-Perron unit is the leading eigenvalue of the action on first integral homology induced by some pseudo-Anosov map. The proof is an application of a construction of Margalit-Spallone. The talk will concentrate on the first result.
This is joint work with my student, Hieu Trung Do.
- Thomas SCHMIDT