An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold

Details An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold

2007-08-03

arxiv.org/abs/0708.0448v2

Mathematics

Geometric Topology

30 pages, no figures

Scientific paper

Using the knot Floer homology filtration, we define invariants associated to a knot in a three-manifold possessing non-vanishing Floer co(homology) classes. In the case of the Ozsvath-Szabo contact invariant we obtain an invariant of knots in a contact three-manifold. This invariant provides an upper bound for the Thurston-Bennequin plus rotation number of any Legendrian realization of the knot. We use it to demonstrate the first systematic construction of prime knots in contact manifolds other than the three-sphere with negative maximal Thurston-Bennequin invariant. Perhaps more interesting, our invariant provides a criterion for an open book to induce a tight contact structure. A corollary is that if a manifold possesses contact structures with distinct non-vanishing Ozsvath-Szabo invariants, then any fibered knot can realize the classical Eliashberg-Bennequin bound in at most one of these contact structures.

Affiliated with

Also associated with

No associations

Rating

An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-601753