Mapping Class Group Action on de Rahm Classes

Venue:
Geb. 20.30, SR 2.058

Date:
25.01.2024
 Speaker:

Time:
15:45 Uhr

Abstract: This talk is about the action of the mapping class group of a hyperbolic surface on de Rahm classes of that surface: in the late 80s, Barge and Ghys proved that the second bounded cohomology group of a closed hyperbolic surface contains an infinitedimensional subspace. Their work is based on the explicit construction of distinct classes, called de Rahm classes, described via differential 2forms. The mapping class group of a surface naturally acts on the second bounded cohomology group of that surface and such action restricts to an action on de Rahm classes.
After reviewing all these objects, we will see how to study this action, interpreting it in a slightly different context. The main goal is to find out all the possible fixed points. By the end of the talk, we will see how this work may be used to study the action of the automorphism group of a surface group on the space of quasimorphism of that surface group.
This is a joint work with Giuseppe Bargagnati, Pietro Capovilla and Francesco Milizia.