Contact surgery and supporting open books
نویسندگان
چکیده
منابع مشابه
Open Books Supporting Overtwisted Contact Structures and Stallings Twist
We study open books (or open book decompositions) of a closed oriented 3-manifold which support overtwisted contact structures. We focus on a simple closed curve along which one can perform Stallings twist, called “twisting loop”. We show that the existence of a twisting loop on the fiber surface of an open book is equivalent up to positive stabilization to the existence of an overtwisted disk ...
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The aim of this paper is to give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. This theorem asserts that simply-connected five-mani-folds admit a contact structure in every homotopy class of almost contact structures. Our proof uses the open book construction of Giroux.
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We define the reduced Khovanov homology of an open book (S, φ), and we identify a distinguished “contact element” in this group which may be used to establish the tightness of contact structures compatible with (S, φ). Our construction generalizes the relationship between the reduced Khovanov homology of a link and the Heegaard Floer homology of its branched double cover. As an application, we ...
متن کامل2 00 6 Open Books on Contact Five - Manifolds
The aim of this paper is to give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. This theorem asserts that simply-connected five-manifolds admit a contact structure in every homotopy class of almost contact structures. Our proof uses the open book construction of Giroux.
متن کاملContact Homology of Left-handed Stabilizations and Plumbing of Open Books
We show that on any closed contact manifold of dimension greater than 1 a contact structure with vanishing contact homology can be constructed. The basic idea for the construction comes from Giroux. We use a special open book decomposition for spheres. The page is the cotangent bundle of a sphere and the monodromy is given by a left-handed Dehn twist. In the resulting contact manifold we exhibi...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2013
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2013.13.1613