Séminaires : Séminaire de Topologie

Equipe(s) : tga,
Responsables :Catherine Gille et Najib Idrissi
Email des responsables :
Salle : 1016
Adresse :Sophie Germain
Description

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Le séminaire de topologie évolue. Des après-midi de topologie seront organisées tout au long de l'année (en collaboration avec USPN) et nous vous en tiendrons informé(e)s sur cette liste de diffusion.


Orateur(s) Cristina Anghel - Université de Genève,
Titre [K-OS] Coloured Jones and coloured Alexander invariants from two Lagrangians intersected in a symmetric power of a surface
Date02/12/2021
Horaire14:00 à 15:00
Diffusion https://lrobert.perso.math.cnrs.fr/join-kos.html
RésumeThe theory of quantum invariants started with the Jones polynomial and continued with the Reshetikhin–Turaev algebraic construction of invariants. In this context, the quantum group Uq(𝔰𝔩(2)) leads to the sequence of coloured Jones polynomials, and the same quantum group at roots of unity gives the coloured Alexander polynomials.
We construct a unified topological model for these two sequences of quantum invariants. More specifically, we prove that the Nth coloured Jones and Nth coloured Alexander invariants are different specialisations of a state sum of Lagrangian intersections in configuration spaces. As a particular case, we see both Jones and Alexander polynomials from the same intersection pairing in a configuration space.
Secondly, we present a globalised model without state sums. We show that one can read off both coloured Jones and coloured Alexander polynomials of colour N from a graded intersection between two explicit Lagrangians in a symmetric power of the punctured disk.
Salle1016
AdresseSophie Germain
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