Summer School 2024 - Low dimensional Topology

Collection Summer School 2024 - Low dimensional Topology

Organizer(s) Scientific Committee: Greg Kuperberg, Christine Lescop, Gwénaël Massuyeau, Jean-Baptiste Meilhan / Organization Committee: Christine Lescop, Gwénaël Massuyeau, Jean-Baptiste Meilhan

Date(s) 17/06/2024 - 05/07/2024

linked URL https://if-summer2024.sciencesconf.org

00:00:00 / 00:00:00

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On the properties of quantum representations of mapping class groups of surfaces 3

By Renaud Detcherry

The Witten-Reshetikhin-Turaev quantum representations are (families of) projective representations of mapping class groups of surfaces, with striking properties: the Dehn twists have finite image, but the representations have a unitary structure and infinite images. We will give a construction of the SO(3)-variant of WRT representations as part of the TQFTs underlying the SO(3)-Witten-Reshetikihin-Turaev invariants of 3-manifolds. We will discuss two deep theorems about WRT-representations: asymptotic faithfulness and the density of the image. Finally, we will present some results about the AMU conjecture, which explains how pseudo-Anosov mapping classes are detected by quantum representations. We will also give restrictions on the kernel of quantum representations at fixed level.

Information about the video

Date of recording 03/07/2024
Date of publication 07/01/2026
Institution Institut Fourier
Licence CC BY NC ND
Language English
Format MP4

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