Volume 5, issue 2 (2001)

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Generating function polynomials for legendrian links

Lisa Traynor

Geometry & Topology 5 (2001) 719–760

arXiv: math.GT/0110229


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.

contact topology, contact homology, generating functions, legendrian links, knot polynomials
Mathematical Subject Classification 2000
Primary: 53D35
Secondary: 58E05
Forward citations
Received: 15 June 2001
Revised: 6 September 2001
Accepted: 5 October 2001
Published: 11 October 2001
Proposed: Yasha Elaishberg
Seconded: Joan Birman, Robion Kirby
Lisa Traynor
Mathematics Department
Bryn Mawr College
Bryn Mawr
Pennsylvania 19010