Invariants of Legendrian knots in circle bundles

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Let E be a circle bundle over a Riemann surface that supports a contact structure transverse to the fibers. This paper presents a combinatorial definition of a differential graded algebra (DGA) that is an invariant of Legendrian knots in E. The invariant generalizes Chekanov's combinatorial DGA invariant of Legendrian knots in the standard contact 3-space using ideas from Eliashberg, Givental, and Hofer's contact homology. The main difficulty lies in dealing with what are ostensibly 1-parameter families of generators for the DGA; these are solved using ``Morse-Bott'' techniques. As an application, the invariant is used to distinguish two Legendrian knots that are smoothly isotopic, realize a non-trivial homology class, but are not Legendrian isotopic.
49 pages, 39 figures

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Symplectic Geometry, Geometric Topology, 57M27; 57R17; 53D40

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http://salesiana.dossiersoluciones.com/handle/123456789/64788

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0208214
 http://arxiv.org/abs/math/0208214

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arXiv