Heegaard Diagrams and Holomorphic Disks

Ozsváth, Peter; Szabó, Zoltán

doi:10.1007/0-306-48658-x_7

Cited by 23 publications

(13 citation statements)

References 96 publications

(187 reference statements)

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“…This approach is historically backwards, but our main purpose here it set up notation and collect properties of the chain complexes we use throughout the text. For a complete discussion we refer the interested reader to [28][29][30]39] and to [31] for a survey.…”

Section: The Knot Floer Homology Filtrationmentioning

confidence: 99%

An Ozsváth–Szabó Floer homology invariant of knots in a contact manifold

Hedden

2008

Advances in Mathematics

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Using the knot Floer homology filtration, we define invariants associated to a knot in a three-manifold possessing non-vanishing Floer co(homology) classes. In the case of the Ozsváth-Szabó contact invariant we obtain an invariant of knots in a contact three-manifold. This invariant provides an upper bound for the Thurston-Bennequin plus rotation number of any Legendrian realization of the knot. We use it to demonstrate the first systematic construction of prime knots in contact manifolds other than S 3 with negative maximal Thurston-Bennequin invariant. Perhaps more interesting, our invariant provides a criterion for an open book to induce a tight contact structure. A corollary is that if a manifold possesses contact structures with distinct non-vanishing Ozsváth-Szabó invariants, then any fibered knot can realize the classical Eliashberg-Bennequin bound in at most one of these contact structures.

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Section: The Knot Floer Homology Filtrationmentioning

confidence: 99%

An Ozsváth–Szabó Floer homology invariant of knots in a contact manifold

Hedden

2008

Advances in Mathematics

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“…We could proceed in this manner to analyze the other (p, q, r)-levels. There is, however, a quicker argument which allows us to determine the link Floer homology polytope with little extra work (proving non-triviality of HFL(L, (p, q, r)) at the remaining points (p, q, r) where at most one of the coordinates vanishes, building on the calculations from equations (20) and (21).…”

Section: Proof Of Propositionmentioning

confidence: 99%

Link Floer homology and the Thurston norm

Ozsváth

Szabó

2008

J. Amer. Math. Soc.

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“…We say the knot Floer homology of a link is monic, if the topmost term is isomorphic to Z. Ozsváth and Szabó proved that if the link is fibred, then the knot Floer homology is monic ( [8], see also [5]). Thus we naturally have the following conjecture (see [10]):…”

Section: Theorem Suppose L Is An Oriented Link In S 3 Let χ(L) Be Tmentioning

confidence: 98%

Closed 3-Braids Are Nearly Fibred

2009

J. Knot Theory Ramifications

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Heegaard Diagrams and Holomorphic Disks

Cited by 23 publications

References 96 publications

An Ozsváth–Szabó Floer homology invariant of knots in a contact manifold

An Ozsváth–Szabó Floer homology invariant of knots in a contact manifold

Link Floer homology and the Thurston norm

Closed 3-Braids Are Nearly Fibred

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