Giorgio Mangioni

Heriot-Watt University


Rigidity properties of mapping class groups and their random quotients


Geometry and Topology Seminar


15th October 2024, 2:00 pm – 3:00 pm
Fry Building, 2.04


A theorem of Ivanov states that the mapping class group G of a finite-type surface is also the automorphism group of the curve graph, which is a graph encoding the intersection patterns of simple closed curves on the surface. This fact can then be used to prove other "rigidity" results, such as quasi-isometric rigidity (if a group "looks like" G, it is a finite index subgroup of G) and the fact that every automorphism of G is inner.

In this talk, we first introduce the various characters in our story, and review the literature on these results. Then we show that the same type of properties are enjoyed by "random" quotients of mapping class groups, defined using random walks on the group.






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