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.
Lisa Traynor. "Generating function polynomials for legendrian links." Geom. Topol. 5 (2) 719 - 760, 2001. https://doi.org/10.2140/gt.2001.5.719