Sebastian Hensel: Fine Curve Graphs and Fragmentation III

Groupes énormes/ Huge Groups (avril/April 03-06, 2023)

Avril/April 05:

The curve graph is a combinatorial object encoding the intersection patterns of simple closed curves on surfaces. It is easy to define, looks at first glance very unwieldy, and has in the last decades proven to be surprisingly useful in geometric group theory, 3-dimensional topology, complex analysis and many more. In this series of talks we will discuss a recent "fine" variant of the curve graph which can be used to answer questions about homeomorphism groups of surface (as opposed to "just" mapping class groups). We will begin with some basics about usual and fine curve graphs, quasimorphisms, and then discuss the proof that the fragmentation norm on the homeomorphism groups of surfaces with genus at least 1 is unbounded (joint work with Jonathan Bowden and Richard Webb). Time permitting we will then discuss newer developments on the large scale geometry of fine curve graphs.