Invariants of Legendrian knots in circle bundles
| dc.creator | Sabloff, Joshua M. | |
| dc.date | 2002-08-27 | |
| dc.date.accessioned | 2026-07-07T04:50:25Z | |
| dc.date.available | 2026-07-07T04:50:25Z | |
| dc.description | 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. | |
| dc.description | 49 pages, 39 figures | |
| dc.identifier | https://arxiv.org/abs/math/0208214 | |
| dc.identifier | http://arxiv.org/abs/math/0208214 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64788 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M27; 57R17; 53D40 | |
| dc.title | Invariants of Legendrian knots in circle bundles | |
| dc.type | text |