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VIRTUAL (Zoom): A homological model for quantum braid representations and colored Jones polynomials, I

Posted in
Speaker: 
Jules Martel
Zugehörigkeit: 
Toulouse
Datum: 
Mon, 2020-05-11 15:00 - 16:00
Parent event: 
MPIM Topology Seminar

Zoom meeting ID: 919-9946-8404
Password: see email announcement or contact the seminar organisers

Abstract: A construction based on Drinfel'd's definition of quantum
groups produces representations for braid groups. Their extensions to
knot invariants, due to Reshetikhin--Turaev, recover the famous Jones
polynomial for instance. The topological meaning of these algebraic
constructions is often missing in the end. In this work we provide a
homological model for quantum representations of braids, adapted from
Lawrence theory. It is based on relative homologies of configuration
spaces of points with local coefficients. This model reaches the level
of knots as it offers an interpretation for colored Jones polynomials in
terms of Lefschetz numbers. This will be presented in the first part,
while in the second one we will pay attention to the quantum algebra
action. After an algebraic study of it, we will build its homological
analogue.

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