$U_q(sl(2))-$quantum invariants unified via intersections of embedded Lagrangians

Cristina Ana-Maria Anghel

Published 2020-10-12Version 1

In this paper we prove a unified model for $U_q(sl(2))$ quantum invariants through intersections of embedded Lagrangians in configuration spaces. More specifically, we construct a state sum of Lagrangian intersections in the configuration space in the punctured disc, which leads to a polynomial in three variables. This polynomial recovers the coloured Jones polynomial and the coloured Alexander polynomial through certain specialisation of coefficients.