$U_q(sl(2))$-quantum invariants from an intersection of two Lagrangians in a symmetric power of a surface
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- by Cristina Ana-Maria Anghel
- Trans. Amer. Math. Soc. 376 (2023), 7139-7185
- DOI: https://doi.org/10.1090/tran/8962
- Published electronically: July 6, 2023
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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 $N^{th}$ coloured Jones and $N^{th}$ 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.References
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Bibliographic Information
- Cristina Ana-Maria Anghel
- Affiliation: University of Geneva, Section de mathématiques, Rue du Conseil-Général 7-9, Geneva CH 1205, Switzerland; and Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania
- MR Author ID: 1453438
- Email: Cristina.Palmer-Anghel@unige.ch; cranghel@imar.ro
- Received by editor(s): February 28, 2022
- Received by editor(s) in revised form: November 26, 2022, March 10, 2023, and March 27, 2023
- Published electronically: July 6, 2023
- Additional Notes: The author was supported by SwissMAP, a National Centre of Competence in Research funded by the Swiss National Science Foundation as well as the Romanian Ministry of Education and Research, grant CNCS-UEFISCDI, project number PN-III-P4-ID-PCE-2020-2798.
- © Copyright 2023 by the author
- Journal: Trans. Amer. Math. Soc. 376 (2023), 7139-7185
- MSC (2020): Primary 57K10; Secondary 57K14
- DOI: https://doi.org/10.1090/tran/8962
- MathSciNet review: 4636687