On the contact class in Heegaard Floer homology

By K. Honda, W. Kazez, G. Matić. 2006

107 citations recorded by the source corpus.

We present an alternate description of the Ozsvath-Szabo contact class in Heegaard Floer homology. Using our contact class, we prove that if a contact structure (M,\xi) has an adapted open book decomposition whose page S is a once-punctured torus, then the monodromy is right-veering if and only if the contact structure is tight.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/95b49bf5059e4c72e4004bb9fcadd1155c5f92e8

How researchers see this paper

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In Geometry and Topology

1. A. Stipsicz
2. John A. Baldwin
3. P. Lisca
4. Peter S. Ozsv'ath
5. Zolt'an Szab'o
6. J. Greene
7. Ciprian Manolescu
8. M. Hedden

In Mathematical Physics

1. A. Stipsicz
2. John A. Baldwin
3. P. Lisca
4. Peter S. Ozsv'ath
5. Zolt'an Szab'o
6. Ciprian Manolescu
7. J. Greene
8. M. Hedden

In Neurology

1. A. Stipsicz
2. Peter S. Ozsv'ath
3. Zolt'an Szab'o
4. John A. Baldwin
5. P. Lisca
6. M. Hedden
7. Ian Zemke
8. Ciprian Manolescu

Citations in the corpus

• Heegaard Floer homology and genus one, one‐boundary component open books (2008, methodology): “The theorem below is a combination of results from [1] and [11], and will be helpful in the proof of Theorem 4.”
• Contact surgeries and the transverse invariant in knot Floer homology (2008, methodology): “In our arguments we will use only the construction of these maps (given by counting holomorphic triangles) and the exactness of the triangle associated to a distinguished triangle.”
• Planar open books, monodromy factorizations and symplectic fillings (2009, unknown): “By contrast, recall that a contact structure supported by an open book of genus one with one boundary component is tight if this particular open book is right-veering [15]; one can hope that since planar open books are another very special case, some sufficient conditions for a given monodromy to en”
• Heegard Floer invariants of Legendrian knots in contact three-manifolds (2008, background): “ [34], which leads to a different Heegaard diagram. It can be shown that the two invariants are identified after a sequence of handleslides; though one can work directly with the above definition, as in [19]. We adopt this point of view, supplying an alternative proof of the invariance of the contact c”