Twisting in small and big mapping class groups

Diana Hubbard, CUNY
Fine Hall 314

In-Person and Online Talk

For a finite type surface with boundary, the fractional Dehn twist coefficient is a rational number that measures, informally, the amount of twisting a mapping class of the surface effects about a chosen boundary component. This quantity has connections to classical knot theory, open book decompositions, and contact geometry. In this talk I will discuss joint work with Peter Feller and Hannah Turner related to this notion: we generalize it to the infinite type setting by characterizing it as the unique quasimorphism from the mapping class group of the surface to the real numbers with certain properties. Unlike in the finite type setting, we can show that for certain infinite type surfaces this quasimorphism is surjective, and I will discuss how this work may be of use in the search for "Nielsen-Thurston"-type classification results for infinite type surfaces.