ISSN:
1432-1807
Keywords:
Mathematics Subject Classification (1991): 57M25,53C15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. We show that every unframed knot type in $ST^*{\bf \mathrm{R}}^2$ has a representative obtained by the Legendrian lifting of an immersed plane curve. This gives a positive answer to the question asked by 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 defined 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00004407
