Generating function polynomials for legendrian links

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

Mathematical Subject Classification 2000

Primary: 53D35

Secondary: 58E05

References

Forward citations

Publication

Received: 15 June 2001

Revised: 6 September 2001

Accepted: 5 October 2001

Published: 11 October 2001

Proposed: Yasha Elaishberg

Seconded: Joan Birman, Robion Kirby

Authors

Lisa Traynor
Mathematics Department Bryn Mawr College Bryn Mawr Pennsylvania 19010 USA

Volume 5, issue 2 (2001)

Lisa Traynor