𝑈_{𝑞}(𝑠𝑙(2))-quantum invariants from an intersection of two Lagrangians in a symmetric power of a surface

Author:

Anghel Cristina

Abstract

In this paper we show that coloured Jones and coloured Alexander polynomials can both be read off from the same picture provided by two Lagrangians in a symmetric power of a surface. More specifically, the N t h N^{th} coloured Jones and N t h N^{th} coloured Alexander polynomials are specialisations of a graded intersection between two explicit Lagrangian submanifolds in a symmetric power of the punctured disc. The graded intersection is parametrised by the intersection points between these Lagrangians, graded in a specific manner using the diagonals of the symmetric power. As a particular case, we see the original Jones and Alexander polynomials as two specialisations of a graded intersection between two Lagrangians in a configuration space, whose geometric supports are Heegaard diagrams.

Funder

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference20 articles.

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3. C. Anghel, Coloured Jones and Alexander polynomials as topological intersections of cycles in configuration spaces, arXiv:2002.09390, [math.GT], 2020, 47 pages.

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5. N. Dowlin, A spectral sequence from Khovanov homology to knot Floer homology, arXiv:1811.07848v1, [math.GT], 2018, 44 pages.

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