PseudoAnosov mapping classes from a symplectic point of view
PseudoAnosov mapping classes from a symplectic point of view

Shaoyun Bai, Princeton University
Fine Hall 314
InPerson Talk
Given a surface diffeomorphism representing a pseudoAnosov mapping class, the number of fixed points of its iterations grows exponentially. This property actually distinguishes pseudoAnosov classes from other ones. For a pair of noncontractible simple curves on a surface with geometric intersection number at least 3, the composition of their Dehn twists defines a pseudoAnosov mapping class according to Thurston. I will explain how to understand this fact using symplectic geometry and discuss its generalization in higher dimensions using the PicardLefschetz theory.