Braided open book decompositions in $S^3$

Torsion and Open Book Decompositions

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.

Detecting tightness via open book decompositions

As the title indicates, the setting is the world of contact structures on, and open book decompositions of, three-manifolds. Throughout, M will refer to a smooth, closed, orientable three-manifold, and ξ a contact structure on M ; that is to say that ξ = ker(α), where α is a globally defined 1-form satisfying the condition that α ∧ dα is a volume form on M . An open book decomposition of M is a...

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 ...

Planar Open Book Decompositions and Contact Structures

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.

Symplectic Cobordisms and Open Book Decompositions