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- W4287642279 abstract "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 {em state sum of Lagrangian intersections in the configuration space in the punctured disc}, which is a polynomial in three variables. It {em recovers the coloured Jones polynomial and the coloured Alexander polynomial} through specialisations of coefficients. This formula works for oriented links coloured with the same representation of the quantum group and can be evaluated at roots of unity. As a corollary, the Jones and Alexander polynomials come both as {em specialisations of an intersection pairing between embedded Lagrangians} in configuration spaces, which is suitable for computations. In particular, we obtain the {em first intersection model for the Jones polynomial} from intersections between submanifolds which are given by {em arcs and circles} in the punctured disc." @default.
- W4287642279 created "2022-07-25" @default.
- W4287642279 creator A5039415321 @default.
- W4287642279 date "2020-10-12" @default.
- W4287642279 modified "2023-09-27" @default.
- W4287642279 title "$U_q(sl(2))-$quantum invariants unified via intersections of embedded Lagrangians" @default.
- W4287642279 doi "https://doi.org/10.48550/arxiv.2010.05890" @default.
- W4287642279 hasPublicationYear "2020" @default.
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