Ozsváth–Szábo invariants and tight contact three-manifolds I

Lisca, Paolo; Stipsicz, András I

doi:10.2140/gt.2004.8.925

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Ozsváth–Szábo invariants and tight contact three-manifolds I

Paolo Lisca and András I Stipsicz

Geometry & Topology 8 (2004) 925–945

DOI: 10.2140/gt.2004.8.925

arXiv: math.SG/0404135

Abstract

Let $S_{r}^{3} (K)$ be the oriented 3–manifold obtained by rational $r$ –surgery on a knot $K \subset S^{3}$ . Using the contact Ozsváth–Szabó invariants we prove, for a class of knots $K$ containing all the algebraic knots, that $S_{r}^{3} (K)$ carries positive, tight contact structures for every $r \neq 2 g_{s} (K) - 1$ , where $g_{s} (K)$ is the slice genus of $K$ . This implies, in particular, that the Brieskorn spheres $- Σ (2, 3, 4)$ and $- Σ (2, 3, 3)$ 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

tight, fillable contact structures, Ozsváth–Szabó invariants

Mathematical Subject Classification 2000

Primary: 57R17

Secondary: 57R57

References

Forward citations

Publication

Received: 21 February 2004

Accepted: 29 May 2004

Published: 9 June 2004

Proposed: Peter Ozsváth

Seconded: John Morgan, Tomasz Mrowka

Authors

Paolo Lisca
Dipartimento di Matematica Università di Pisa I-56127 Pisa Italy

András I Stipsicz
Rényi Institute of Mathematics Hungarian Academy of Sciences H-1053 Budapest Reáltanoda utca 13–15 Hungary

Volume 8, issue 2 (2004)