Séminaire Géométries ICJ

Genericity of pseudo-Anosov mapping classes, when seen as mapping classes

par Juan Souto

Europe/Paris
Description
 According to Thurston, elements in the mapping class group can be Pseudo-Anosov, reducible, or finite order. In the particular case of the once punctured torus, where the mapping class group is nothing other than SL_2Z, Pseudo-Anosov elements correspond to diagonalisable elements whose eigenvalues have norm other than 1. Anyways, it is suspected that Pseudo-Anosov elements are generic. In fact, is known that a random walk (of say full support) in the mapping class group produces pseudo-Anosov elements with probability tending to 1, but there are many other ways in which pseudo-Anosov elements are suspected to be generic. In this talk I will explain why they are generic when we remember that the mapping class group is made out of mapping classes. This is joint work with V. Erlandsson and J. Tao.