Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves
type: Item
instance of: scholarly article
title: Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves
zbMATH Open document ID: 0957.57005
DOI: 10.1007/PL00004407
published in: Mathematische Annalen
publication date: 2001-03-22T00:00:00Z
review text: The authors extend parallels between regular plane curves and knots, based on approaches due to Arnold and Vassiliev. It is shown that any unframed knot type in the solid torus \(ST^{*}{\mathbb R}^2\) has a representative obtained by the Legendrian lifting of an immersed plane curve. This gives a positive answer to the question asked by \textit{V. I.~Arnol'd} [Topological invariants of plane curves and caustics, Univ. Lect. Ser. 5 (1994; Zbl 0858.57001)]. Also, restrictions of the Legendrian framings of such lifts are investigated. It is shown that there is an estimate of these framings which comes from the HOMFLY polynomial of a knot in a solid torus, and this is often stronger than Bennequin's inequality.
reviewed by: Andrei Vesnin
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 1502092
zbMATH Keywords: framed knots
author: S. Chmutov
author: V. V. Goryunov
author: Hitoshi Murakami
MaRDI profile type: Publication
full work available at URL: s002080000057
OpenAlex ID: W4312490468
description: scientific article; zbMATH DE number 1502092