2020/10/12 by Cristina Ana-Maria Anghel, Anghel, Cristina Ana-Maria · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2010.05890
In this paper we prove a unified model for Uq(sl(2)) quantum invariants\nthrough intersections of embedded Lagrangians in configuration spaces. More\nspecifically, we construct a em state sum of Lagrangian intersections in the\nconfiguration space in the punctured disc, which is a polynomial in three\nvariables. It em recovers the coloured Jones polynomial and the coloured\nAlexander polynomial through specialisations of coefficients. This formula\nworks for oriented links coloured with the same representation of the quantum\ngroup and can be evaluated at roots of unity. As a corollary, the Jones and\nAlexander polynomials come both as em specialisations of an intersection\npairing between embedded Lagrangians in configuration spaces, which is\nsuitable for computations. In particular, we obtain the em first intersection\nmodel for the Jones polynomial from intersections between submanifolds which\nare given by em arcs and circles in the punctured disc.\n