Ozsvath-Szabo invariants and tight contact three-manifolds, II
Symplectic Geometry
2007-05-23 v4 Geometric Topology
Abstract
Let p and n be positive integers with p>1, and let E(p,n) be the oriented 3-manifold obtained by performing pn(p-1)-1 surgery on a positive torus knot of type (p, pn+1). We prove that E(2,n) does not carry tight contact structures for any n, while E(p,n) carries tight contact structures for any n and any odd p. In particular, we exhibit the first infinite family of closed, oriented, irreducible 3-manifolds which do not support tight contact structures. We obtain the nonexistence results via standard methods of contact topology, and the existence results by using a quite delicate computation of contact Ozsvath-Szabo invariants.
Keywords
Cite
@article{arxiv.math/0404136,
title = {Ozsvath-Szabo invariants and tight contact three-manifolds, II},
author = {Paolo Lisca and Andras I. Stipsicz},
journal= {arXiv preprint arXiv:math/0404136},
year = {2007}
}
Comments
35 pages, 10 figures, very small changes