Ozsváth-Szabó invariants and tight contact three-manifolds, I

Paolo Lisca, A. Stipsicz

Research output: Article

39 Citations (Scopus)

Abstract

Let Sr3(K) be the oriented 3-manifold obtained by rational r-surgery on a knot K ⊂ S3. Using the contact Ozsváth-Szabó invariants we prove, for a class of knots K containing all the algebraic knots, that Sr3 (K) carries positive, tight contact structures for every r ≠ 2gs(K) - 1, where gs(K) is the slice genus of K. This implies, in particular, that the Brieskorn spheres -∑(2, 3, 4) and -∑(2, 3, 3) carry tight, positive contact structures. As an application of our main result we show that for each m ∈ ℕ there exists a Seifert fibered rational homology 3-sphere M m carrying at least m pairwise non-isomorphic tight, non fillable contact structures.

Original languageEnglish
Pages (from-to)925-945
Number of pages21
JournalGeometry and Topology
Volume8
Publication statusPublished - 2004

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Three-manifolds
Contact Structure
Knot
Contact
Invariant
Slice
Surgery
Homology
Pairwise
Genus
Imply

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Ozsváth-Szabó invariants and tight contact three-manifolds, I. / Lisca, Paolo; Stipsicz, A.

In: Geometry and Topology, Vol. 8, 2004, p. 925-945.

Research output: Article

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