Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves

S. Chmutov, V. Goryunov, H. Murakami

研究成果: Article査読

16 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)389-413
ページ数25
ジャーナルMathematische Annalen
317
3
DOI
出版ステータスPublished - 2000 7月
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

フィンガープリント

「Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル