Tight contact structures and genus one fibered knots

Details Tight contact structures and genus one fibered knots Tight contact structures and genus one fibered knots

2006-04-26

arxiv.org/abs/math/0604580v3

Mathematics

Symplectic Geometry

30 pages, 10 figures. Added figures, extended result to all monodromies, and added sections 5 and 6

Scientific paper

We study contact structures compatible with genus one open book decompositions with one boundary component. Any monodromy for such an open book can be written as a product of Dehn twists around dual non-separating curves in the once-punctured torus. Given such a product, we supply an algorithm to determine whether the corresponding contact structure is tight or overtwisted. We rely on Ozsv{\'a}th-Szab{\'o} Heegaard Floer homology in our construction and, in particular, we completely identify the $L$-spaces with genus one, one boundary component, pseudo-Anosov open book decompositions. Lastly, we reveal a new infinite family of hyperbolic three-manifolds with no co-orientable taut foliations, extending the family discovered in \cite{RSS}.

Affiliated with

Also associated with

No associations

Rating

Tight contact structures and genus one fibered knots 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 Tight contact structures and genus one fibered knots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tight contact structures and genus one fibered knots will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-20922