Geometry & Topology, Vol. 5 (2001) Paper no. 23, pages 719--760.

Generating function polynomials for legendrian links

Lisa Traynor

Abstract. It is shown that, in the 1-jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component of the links considered is legendrian isotopic to the 1-jet of the 0-function, and thus cannot be distinguished by the classical rotation number or Thurston-Bennequin invariants. The links are distinguished by calculating invariant polynomials defined via homology groups associated to the links through the theory of generating functions. The many calculations of these generating function polynomials support the belief that these polynomials carry the same information as a refined version of Chekanov's first order polynomials which are defined via the theory of holomorphic curves.

Keywords. Contact topology, contact homology, generating functions, legendrian links, knot polynomials

AMS subject classification. Primary: 53D35. Secondary: 58E05.

DOI: 10.2140/gt.2001.5.719

E-print: arXiv:math.GT/0110229

Submitted to GT on 15 June 2001. (Revised 6 September 2001.) Paper accepted 5 October 2001. Paper published 11 October 2001.

Notes on file formats

Lisa Traynor
Mathematics Department, Bryn Mawr College
Bryn Mawr, PA 19010, USA

GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to