Quantum representations of surface groups

Apparaît dans la collection : Summer School 2018 - Teichmüller dynamics, mapping class groups and applications.

I will show how we can produce exotic representations of surface groups from the Witten-Reshetikhin-Turaev TQFT. These representations have infinite images and give points on character varieties that are fixed by the action of the mapping. Moreover we can approximate these representations by representations into finite groups in order to build exotic regular finite covers of surfaces. These covers have the following property: the integral homology is not generated by pullbacks of simple closed curves on the base. This is joint work with Thomas Koberda.