Open book decompositions and stable Hamiltonian structures
نویسندگان
چکیده
منابع مشابه
Open Book Decompositions and Stable Hamiltonian Structures
We show that every open book decomposition of a contact 3–manifold can be represented (up to isotopy) by a smooth R–invariant family of pseudoholomorphic curves on its symplectization with respect to a suitable stable Hamiltonian structure. In the planar case, this family survives small perturbations, and thus gives a concrete construction of a stable finite energy foliation that has been used ...
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In this note we observe that while all overtwisted contact structures on compact 3–manifolds are supported by planar open book decompositions, not all contact structures are. This has relevance to the Weinstein conjecture [1] and invariants of contact structures.
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This theorem plays a pivotal role in studying cobordisms of contact structures and understanding filling properties of contact structures, see [2, 6, 14, 13, 16, 19]. This better understanding of fillings leads to various topological applications of contact geometry. Specifically, the much studied property P for knots was established by Kronheimer and Mrowka in [28]. A non-trivial knot has prop...
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We show that if (B, π) is an open book decomposition of a contact 3–manifold (Y, ξ), then the complement of the binding B has no Giroux torsion. We also prove the sutured Heegaard-Floer c-bar invariant of the binding of an open book is non-zero.
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In this paper, we give an open book decomposition for the contact structures on some Brieskorn manifolds, in particular for the contact structures of Ustilovsky. The decomposition uses right-handed Dehn twists as conjectured by Giroux. 0. Introduction At the ICM of 2002 Giroux announced some of his results concerning a correspondence between contact structures on manifolds and open book structu...
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2010
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2009.09.001