Tight contact structures on some small Seifert fibered 3-manifolds

By P. Ghiggini, P. Lisca, A. Stipsicz. 2005

56 citations recorded by the source corpus.

We classify tight contact structures on the small Seifert fibered 3-manifolds M(−1; r1, r2, r3) with ri ∈ (0, 1) ∩ Q and r1, r2 ≥ ½ . The result is obtained by combining convex surface theory with computations of contact Ozsváth–Szabó invariants. We also show that some of the tight contact structures on the manifolds considered are nonfillable, justifying the use of Heegaard Floer theory.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2fb31ee45ef274242926712c7f6d4ccc733116f6

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In Applied Mathematics

1. Zolt'an Szab'o
2. Peter S. Ozsv'ath
3. A. Stipsicz
4. P. Lisca
5. John B. Etnyre
6. Fan Ding
7. Hansjörg Geiges
8. Jeremy Van Horn-Morris

In Discrete Mathematics and Combinatorics

1. A. Stipsicz
2. P. Lisca
3. Peter S. Ozsv'ath
4. John B. Etnyre
5. Zolt'an Szab'o
6. Jeremy Van Horn-Morris
7. Ciprian Manolescu
8. P. Ghiggini

In Geometry and Topology

1. A. Stipsicz
2. P. Lisca
3. Peter S. Ozsv'ath
4. Zolt'an Szab'o
5. John B. Etnyre
6. P. Ghiggini
7. Jeremy Van Horn-Morris
8. John A. Baldwin

Citations in the corpus

• On the existence of tight contact structures on Seifert fibered 3-manifolds (2007, background): “Tight contact structures up to isotopy are classified on S 3 , lens spaces [15, 18], circle bundles over surfaces [19] and some special Seifert fibered 3–manifolds [11, 12, 13, 14, 35].”
• Planar open books, monodromy factorizations and symplectic fillings (2009, unknown): “) Tight contact structures on such manifolds were studied by Ghiggini–Lisca– Stipsicz [8] and Lisca–Stipsicz [19; 20]; when r1; r2 1=2, a complete classification of tight contact structures on M.”
• Heegard Floer invariants of Legendrian knots in contact three-manifolds (2008, methodology): “The tightness of the result of these latter surgeries was verified in [17] by computing the contact Ozsváth– Szabó invariants of the resulting contact structures.”
• Cabling, contact structures and mapping class monoids (2010, background): “It is known that neither HFH (Σ) nor Weak(Σ) is included in the other, see [28, 29].”
• Grid Homology for Knots and Links (2015, background): “The Heegaard Floer contact invariant is useful for classifying contact structures on specific three-manifolds; see for example [72].”
• Handle moves in contact surgery diagrams (2008, background): “The resulting contact surgery diagrams were studied more carefully in [6] and since then have led — in particular, when combined with Heegaard Floer theory — to a wealth of applications; see, for example, [17], [26], [31].”