Planar open books and Floer homology

By Peter S. Ozsv'ath, A. Stipsicz, Zolt'an Szab'o. 2005

46 citations recorded by the source corpus.

Giroux has described a correspondence between open book decompositions on a 3--manifold and contact structures. In this paper we use Heegaard Floer homology to give restrictions on contact structures which correspond to open book decompositions with planar pages, generalizing a recent result of Etnyre.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e45d3e3cf814e94426c4bcf61b1b8aa28b899aec

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In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Planar open books, monodromy factorizations and symplectic fillings (2009, unknown): “We note that this method is in principle applicable to planar open books, because by Etnyre [5] and Oszváth–Stipsicz–Szabó [24], every symplectic filling of a contact structure supported by a planar open book must be negative-definite, and have the intersection form that embeds into a standard diago”
Ozsvth-Szab invariants and tight contact 3-manifolds, III (2007, background): “Then, according to [8, 31] ξ is not planar.”
A hierarchy of local symplectic filling obstructions for contact $3$-manifolds (2010, background): “cular to all planar contact manifolds and can thus be viewed as an obstruction to planarity. The corresponding obstruction in Heegaard Floer homology is a known result of Ozsvath, Stipsicz and Szabo´ [OSS05]. Our version of the obstruction can easily be strengthened by observing that a planar open b”