Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves

S. Chmutov, V. Goryunov, H. Murakami

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We show that every unframed knot type in ST*R2 has a representative obtained by the Legendrian lifting of an immersed plane curve. This gives a positive answer to the question asked by V.I.Arnold in [3]. The Legendrian lifting lowers the framed version of the HOMFLY polynomial [20] to generic plane curves. We prove that the induced polynomial invariant can be completely denned in terms of plane curves only. Moreover it is a genuine, not Laurent, polynomial in the framing variable. This provides an estimate on the Bennequin-Tabachnikov number of a Legendrian knot.

Original languageEnglish
Pages (from-to)389-413
Number of pages25
JournalMathematische Annalen
Volume317
Issue number3
DOIs
Publication statusPublished - 2000 Jul
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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