Seminar

We will introduce an example due to Fanoni–Hensel of a big mapping class group acting on a hyperbolic graph in which some elements act parabolically. This is a phenomenon that does not occur in the finite-type setting, and it appears to complicate the picture of a Nielsen–Thurston-type classification of homeomorphisms of infinite-type surfaces. This can be viewed in contrast to Mladen’s talk last week, which introduced a natural generalization of periodic homeomorphisms.

The Fanoni–Hensel construction relies on fine curve graph techniques, illustrating the close relationship between fine curve graphs and the dynamics of actions of big mapping class groups. For background, it is recommended (but not necessary) to attend the fine curve graph reading group beforehand.