On the existence of tight contact structures on Seifert fibered 3-manifolds

DOI10.1215/00127094-2009-024zbMath1233.57013arXiv0709.0737OpenAlexW2011210443MaRDI QIDQ1026418

András I. Stipsicz, Paolo Lisca

Publication date: 24 June 2009

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.0737

zbMATH Keywords

Seifert manifoldscontact structuresOzsváth-Szabó invariantHeegard-Floer homology

Mathematics Subject Classification ID

Symplectic and contact topology in high or arbitrary dimension (57R17) Global theory of symplectic and contact manifolds (53D35) Surgery and handlebodies (57R65) Floer homology (57R58)

Related Items (20)

Instanton Floer homology and contact structures ⋮ Fillability of small Seifert fibered spaces ⋮ Contact Structures and Geometric Topology ⋮ A note on the knot Floer homology of fibered knots ⋮ Hyperbolic 3-manifolds admitting no fillable contact structures ⋮ Planar open books, monodromy factorizations and symplectic fillings ⋮ Tight contact structures on hyperbolic three-manifolds ⋮ Residual torsion-free nilpotence, biorderability and pretzel knots ⋮ Stein fillable Seifert fibered 3-manifolds ⋮ Tightness in contact metric 3-manifolds ⋮ Non-loose negative torus knots ⋮ Infinitely many universally tight torsion free contact structures with vanishing Ozsváth-Szabó contact invariants ⋮ On the \overline{𝜇}–invariant of rational surface singularities ⋮ Tight small Seifert fibered manifolds with \(e_0= -2\) ⋮ Tour of bordered Floer theory ⋮ Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions ⋮ Classification of tight contact structures on small Seifert fibered \(L\)-spaces ⋮ Classification of tight contact structures on surgeries on the figure-eight knot ⋮ Complementary legs and rational balls ⋮ Floer theory and its topological applications

Cites Work

• Unnamed Item
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• Ozsváth-Szabó invariants and tight contact three-manifolds. II
• Ozsváth-Szabó invariants and tight contact 3-manifolds, III
• Transverse foliations of Seifert bundles and self homeomorphism of the circle
• Convexité en topologie de contact. (Convexity in contact topology)
• Symplectic fillings and positive scalar curvature
• Handlebody construction of Stein surfaces
• On the Floer homology of plumbed three-manifolds
• On the classification of tight contact structures. I
• On the classification of tight contact structures. II.
• Transverse contact structures on Seifert 3-manifolds
• Holomorphic disks and topological invariants for closed three-manifolds
• Holomorphic disks and three-manifold invariants: properties and applications
• Classification of overtwisted contact structures on 3-manifolds
• On the nonexistence of tight contact structures
• Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary
• Seifert fibered contact three-manifolds via surgery
• Ozsváth-Szabó invariants and tight contact three-manifolds; I
• Deformationen von Quotientensingularitäten (nach zyklischen Gruppen)
• On tight contact structures with negative maximal twisting number on small Seifert manifolds
• Milnor open books and Milnor fillable contact 3-manifolds
• Holomorphic triangles and invariants for smooth four-manifolds
• Heegaard Floer homology and contact structures
• Tight contact structures on Seifert manifolds over \(T^2\) with one singular fibre
• A Legendrian surgery presentation of contact 3-manifolds
• Tight contact structures on some small Seifert fibered 3-manifolds
• LEGENDRIAN VERTICAL CIRCLES IN SMALL SEIFERT SPACES
• Classification of tight contact structures on small Seifert 3–manifolds with 𝑒₀≥0
• Foliations and the topology of 3-manifolds
• Symplectic fillability of tight contact structures on torus bundles

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