Planar open books, monodromy factorizations, and symplectic fillings

Abstract

We study fillings of contact structures supported by planar open books by analyzing positive factorizations of their monodromy. Our method is based on Wendl's theorem on symplectic fillings of planar open books. We prove that every virtually overtwisted contact structure on L(p,1) has a unique filling, and describe fillable and non-fillable tight contact structures on certain Seifert fibered spaces.

20 pages, 13 figures

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
• Planar open book decompositions and contact structures
• Planar open books and Floer homology

Cited by in corpus (19)

• Weak Symplectic Fillings and Holomorphic Curves
• A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
• Calabi-Yau Caps, Uniruled Caps and Symplectic Fillings
• Fillings of unit cotangent bundles
• Positive factorizations of mapping classes
• On Stein fillings of contact torus bundles
• Contact structures and reducible surgeries
• Stein fillings of contact 3-manifolds obtained as Legendrian surgeries
• Contact 3-manifolds, holomorphic curves and intersection theory
• Fillings of unit cotangent bundles of nonorientable surfaces
• On contact type hypersurfaces in 4-space
• Generalizations of planar contact manifolds to higher dimensions
• Tight Planar Contact Manifolds with Vanishing Heegaard Floer Contact Invariants
• Fillability of small Seifert fibered spaces
• On symplectic fillings of virtually overtwisted torus bundles
• Stein fillings of homology $3$-spheres and mapping class groups
• Stein-fillable open books of genus one that do not admit positive factorisations
• Proportion of cyclic matrices in maximal reducible matrix algebras
• Classification of genus-$1$ holomorphic Lefschetz pencils