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
Email: ltraynor@brynmawr.edu
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