Derivation of the HOMFLYPT knot polynomial via helicity and geometric quantization

Mauro Spera; Antonio Michele Miti

doi:10.1007/s40574-020-00254-5

Derivation of the HOMFLYPT knot polynomial via helicity and geometric quantization

Mauro Spera, Antonio Michele Miti

Risultato della ricerca: Contributo in rivista › Articolo in rivista › peer review

Abstract

In this note we propose a geometric quantization interpretation of the HOMFLYPT polynomial, taking inspiration from the Liu-Ricca hydrodynamical approach to the latter and building on the Besana-S. symplectic approach to framing via Brylinski’s manifold of mildly singular links.

Lingua originale	English
pagine (da-a)	269-284
Numero di pagine	16
Rivista	BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA
Volume	14
DOI	https://doi.org/10.1007/s40574-020-00254-5
Stato di pubblicazione	Pubblicato - 2021

Keywords

Knot polynomials, symplectic geometry, Lagrangian submanifolds, hydrodynamics, geometric quantization, Maslov index.

Accesso al documento

10.1007/s40574-020-00254-5

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abstract = "In this note we propose a geometric quantization interpretation of the HOMFLYPT polynomial, taking inspiration from the Liu-Ricca hydrodynamical approach to the latter and building on the Besana-S. symplectic approach to framing via Brylinski{\textquoteright}s manifold of mildly singular links.",

keywords = "Knot polynomials, symplectic geometry, Lagrangian submanifolds, hydrodynamics, geometric quantization, Maslov index., Knot polynomials, symplectic geometry, Lagrangian submanifolds, hydrodynamics, geometric quantization, Maslov index.",

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AB - In this note we propose a geometric quantization interpretation of the HOMFLYPT polynomial, taking inspiration from the Liu-Ricca hydrodynamical approach to the latter and building on the Besana-S. symplectic approach to framing via Brylinski’s manifold of mildly singular links.

KW - Knot polynomials, symplectic geometry, Lagrangian submanifolds, hydrodynamics, geometric quantization, Maslov index.

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DO - 10.1007/s40574-020-00254-5

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JO - Bolletino dell Unione Matematica Italiana

JF - Bolletino dell Unione Matematica Italiana

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