Gluing tight contact structures

By K. Honda. 2001

96 citations recorded by the source corpus.

We prove gluing theorems for tight contact structures. In particular, we rederive (as special cases) gluing theorems due to Colin and Makar-Limanov, and present an algorithm for determining whether a given contact structure on a handlebody is tight. As applications, we construct a tight contact structure on a genus 4 handlebody which becomes overtwisted after Legendrian -1 surgery, and study certain Legendrian surgeries on T^3.

Subfields: Applied Mathematics, Genetics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c662a246de43b391c5d8e420d7425f3d0d9cb531

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In Applied Mathematics

1. John B. Etnyre
2. K. Honda
3. P. Ghiggini
4. G. Matić
5. W. Kazez
6. S. Schoenenberger
7. T. Ekholm
8. A. Stipsicz

In Genetics

1. John B. Etnyre
2. P. Ghiggini
3. S. Schoenenberger
4. G. Matić
5. W. Kazez
6. O. Plamenevskaya
7. Peter S. Ozsv'ath
8. Lenhard L. Ng

In Geometry and Topology

1. K. Honda
2. John B. Etnyre
3. P. Ghiggini
4. A. Stipsicz
5. W. Kazez
6. G. Matić
7. S. Schoenenberger
8. Peter S. Ozsv'ath

Citations in the corpus

• Right-veering diffeomorphisms of compact surfaces with boundary (2005, methodology): “An open book decomposition (S, h, K ) gives rise to a special Heegard decomposition of M. Denote by Hi, i = 1, 2, the two handlebodies H1 = S ×[ 0, 1 ]/∼h and H2 = S × 1 , 1 /∼h . Writing St =”
• Legendrian and Transversal Knots (2003, background): “The answer is NO if the manifold is allowed to have boundary [ 58 ] (cf.”
• Tight contact structures with no symplectic fillings (2000, background): “We thank Yasha Eliashberg for informing us that Legendrian surgery preserves weakly fillable contact structures.”
• The contact invariant in sutured Floer homology (2007, background): “ch takes x′′ to x′ ⊗ x. We are assuming that [x] 6= 0. Also, [ x′] 6= 0 is immediate from the fact that β1 and γ1 intersect only at x′ 1, due to our choice of basis. Therefore, we have [x′′] 6= 0. In [H2], the first author exhibited a tight contact structure on a handlebody which became overtwisted a”
• On the classification of tight contact structures (2002, methodology): “elds fillable contact structures. Hence this strategy is not successful in every case; see [13]. Today, there are methods to construct tight contact structures which are independent of fillability; see [2, 23]. 4.1. The case Σ(2,3,11). In this subsection, M denotes the Brieskorn homology sphere Σ(2,3,”
• On symplectic cobordisms (2001, background): “There is some related material in [20] for Legendrian surgeries.”
• Lectures on open book decompositions and contact structures (2004, background): “Is ξ(L,−1) tight if ξ is tight? If the original contact manifold (M, ξ) is not closed then it is known that the answer is sometimes NO, see [26].”