U_q(sl(2))-quantum invariants from an intersection of two Lagrangians\n in a symmetric power of a surface

2021/11/01 by Cristina Ana-Maria Anghel, Anghel, Cristina Ana-Maria
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2111.01125

openalex publication_date 2021/11/01 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this paper we show that coloured Jones and coloured Alexander polynomials\ncan both be read off from the same picture provided by two Lagrangians in a\nsymmetric power of a surface. More specifically, the N^th coloured Jones\nand N^th coloured Alexander polynomials are specialisations of a graded\nintersection between two explicit Lagrangian submanifolds in a symmetric power\nof the punctured disc. The graded intersection is parametrised by the\nintersection points between these Lagrangians, graded in a specific manner\nusing the diagonals of the symmetric power. As a particular case, we see the\noriginal Jones and Alexander polynomials as two specialisations of a graded\nintersection between two Lagrangians in a configuration space, whose geometric\nsupports are Heegaard diagrams.\n

Citations

• U_q(sl(2))-quantum invariants unified via intersections of embedded\n Lagrangians

Related

• U_q(sl(2))-quantum invariants unified via intersections of embedded\n Lagrangians
• Coloured Jones and Alexander polynomials as topological intersections of cycles in configuration spaces
• A topological model for the coloured Alexander invariants
• A globalisation of Jones and Alexander polynomials constructed from a graded intersection of two Lagrangians in a configuration space
• Geometric universal Jones invariant from configurations on ovals in the disc