Planar Contact Structures with Binding Number Three

Abstract

In this article, we find the complete list of all contact structures (up to isotopy) on closed three-manifolds which are supported by an open book decomposition having planar pages with three (but not less) boundary components. We distinguish them by computing their first Chern classes and three dimensional invariants (whenever possible). Among these contact structures we also distinguish tight ones from those which are overtwisted.

35 pages, 19 figures, 9 tables (published version)

References in corpus (5)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Right-veering diffeomorphisms of compact surfaces with boundary II
• Lectures on open book decompositions and contact structures
• A Legendrian surgery presentation of contact 3-manifolds
• On the support genus of a contact structure

Cited by in corpus (3)

• A note on Mazur type Stein fillings of planar contact manifolds
• On the Classification of Planar Contact Structures
• On overtwisted, right-veering open books