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 . The Legendrian lifting lowers the framed version of the HOMFLY polynomial  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.
ASJC Scopus subject areas
- 数学 (全般)