Ozsvath-Szabo invariants and tight contact three-manifolds, I
Abstract
Let S^3_r(K) be the oriented 3--manifold obtained by rational r-surgery on a knot K in S^3. Using the contact Ozsvath-Szabo invariants we prove, for a class of knots K containing all the algebraic knots, that S^3_r(K) carries positive, tight contact structures for every r not= 2g_s(K)-1, where g_s(K) is the slice genus of K. This implies, in particular, that the Brieskorn spheres -Sigma(2,3,4) and -Sigma(2,3,3) carry tight, positive contact structures. As an application of our main result we show that for each m in N there exists a Seifert fibered rational homology 3-sphere M_m carrying at least m pairwise non-isomorphic tight, nonfillable contact structures.
Keywords
Cite
@article{arxiv.math/0404135,
title = {Ozsvath-Szabo invariants and tight contact three-manifolds, I},
author = {Paolo Lisca and Andras I Stipsicz},
journal= {arXiv preprint arXiv:math/0404135},
year = {2014}
}
Comments
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper24.abs.html