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 de ned 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 re ned version of Chekanov’s rst order polynomials which are de ned via the theory of holomorphic curves. AMS Classi cation numbers Primary: 53D35 Secondary: 58E05