Some examples of (big) mapping classes and their mapping toriMPIM

by Juan Souto (University of Rennes 1)

Thursday Apr 16, 2026, 4:30 PM → 5:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Oberseminar Differentialgeometrie

A mapping class $f:S\to S$ of a surface of finite topological type is pseudo-Anosov if one of the following equivalent conditions holds: (1) no power of $f$ fixes a curve, (2) the mapping torus is pseudo-Anosov, (3) $f$ has a representative which acts as a (singular) affine map with respect to some semi-translational structure on $S$, (4) $f$ acts as a translation along a Teichmueller geodesic, (5) $f$ acts loxodromically on the curve complex, (6) $f$ has north-south dynamics on the space $PML$ of projective measures laminations., (7)... When $S$ has infinite type, things are much more complicated. I will discuss some examples where, what can go well goes well, or at least as well as it can go. This is joint work with Tommaso Cremaschi and Ferrán Valdez.