Tuesday 16 November 2021
Fathi Ben Aribi (Université Catholique de Louvain) — Link invariants from L2-Burau maps of braids
L2-Burau maps of braids are generalizations of the Burau representation of braid groups, that A. Conway and I defined in 2018. The coefficients of the L2-Burau matrices may no longer be Laurent polynomials but instead live in a general non abelian group ring. We previously linked some of these L2-Burau maps to L2-Alexander torsions of links, which are powerful but elusive link invariants.
In this talk, I will go further and provide answers to a natural question: how can one define other link invariants from general L2-Burau maps? To this end, I studied the influence of Markov moves of braids on L2-Burau maps, and I computed new values of L2-determinants via combinatorics on Cayley graphs of groups.
In the first part of the talk I will recall basic facts about braid groups, link invariants, the Burau representation and L2-invariants. In the second part I will go into more details on how to construct link invariants from L2-Burau maps.
* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.