Journées de topologie quantique

The “journées de topologie quantique” (quantum topology days) are a regular event aiming at bringing together, in a somewhat informal setting, people thinking about quantum topology in a broad sense. As the name suggest this is a one day event, with three talks and lots of time for discussions, taking place either in Paris or in Dijon.

Next session: 13 November 2023

Location: Dijon

Precise location and schedule tba


V. Lin, in the 'Kourkova notebook', questions the existence of a non-trivial epimorphism of the braid group onto a non-abelian torsion-free group. The homotopy braid group studied by Goldsmith in 1974 an known to be nilpotent, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than 6 strands. In this presentation, we will see a new approach based on the broader concept of welded braids, as well as algebraic techniques. This will allow us to demonstrate that the homotopy braid group is torsion-free for any number of strands.

Past events

21 November 2022 (Paris)

13 March 2023 (Dijon)

5 June 2023 (Paris)

From the perspective of the Cobordism Hypothesis, this data defines an invertible non-semisimple TQFT varying over the character stack (the moduli space of $G$-local systems) which extends the Crane-Yetter theory. To 3-manifolds this theory assigns a line bundle on the character stack with the fiber over the trivial local system being the non-semisimple Crane-Yetter theory. To surfaces the theory assigns an invertible sheaf of categories on the character stack given by the skein category of the surface, yielding a categorified version of the fact that the skein algebra defines a sheaf on the character variety which is Azumaya over an open dense locus (the locus being precisely determined recently by Karuo-Korinman). Building on recent work of Haïoun on dualizability, we expect to be able to define a non-semisimple $G$-relative version of Witten-Reshetikhin-Turaev theory similar to the contemporary understanding of WRT as relative to CY.