Legendrian knots in overtwisted contact structures
Geometric Topology
2007-05-23 v2
Abstract
We prove that two Legendrian knots in a contact structure which is trivializable as a plane bundle are Legendrian isotopic provided that (1) they are isotopic as framed knots, (2) they have the same rotation number with respect to some parallelization of the contact structure, and (3) there is an overtwisted disk disjoint with both knots. (For zero-homologous knots the condition (1) reads as: (1a) they are isotopic as topological knots, and (1b) they have the same Thurston-Bennequin invariant.) Then we discuss the situation when condition (3) is not fulfilled, in particular that of non-loose Legendrian knots.
Cite
@article{arxiv.math/0410122,
title = {Legendrian knots in overtwisted contact structures},
author = {Katarzyna Dymara},
journal= {arXiv preprint arXiv:math/0410122},
year = {2007}
}
Comments
34 pages, 29 figures; uses eplain and epsf. Minor corrections, figures fixed, references updated