LiT II: Lost in Topology

TOPOLOGICAL MODELS FOR Uq(sl(2)) QUANTUM INVARIANTS

speaker: Cristina Ana Maria (MINICOURSE) Anghel (University of Leeds    )

abstract: Quantum topology started with the Jones polynomial and it was developed by Witten- Reshetikhin-Turaev’s algebraic machinery of defining quantum invariants. In this context, the quantum group Uq(sl(2)) leads to two sequences of link invariants: coloured Jones polynomials and coloured Alexander polynomials. The geometry and topology encoded by these invariants are the subjects of important open problems in quantum topology. In this series of lectures we will construct a new topological viewpoint that sees these invariants purely through the topology of configuration spaces. We show that both Jones and Alexander polynomials can be seen from a common perspective based on configurations on ovals and arcs in the disc. Secondly, we discuss a unified topological model for their quantum generalisations, proving that coloured Jones and Alexander polynomials can be read off from Lagrangian intersections in a fixed configuration space. The third part concerns a topological perspective on the asymptotic behaviour of these invariants when the colour tends to infinity. If time permits, we pass to the level of 3-manifolds presenting a topological model for the Witten-Reshetikhin-Turaev invariants.

timetable:
Tue 17 Sep, 9:00 - 10:00, Aula Dini
Wed 18 Sep, 11:30 - 12:30, Aula Dini
Thu 19 Sep, 9:00 - 10:00, Aula Dini
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