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 (10)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• On the classification of tight contact structures I
• Right-veering diffeomorphisms of compact surfaces with boundary II
• Lectures on open book decompositions and contact structures
• Strongly Fillable Contact Manifolds and J-holomorphic Foliations
• On the existence of tight contact structures on Seifert fibered 3-manifolds
• Handle moves in contact surgery diagrams
• Planar open book decompositions and contact structures
• Planar open books and Floer homology
• Right-veering diffeomorphisms of compact surfaces with boundary I

Cited by in corpus (20)

• 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
• Positive factorizations of mapping classes
• On Stein fillings of contact torus bundles
• Fillings of unit cotangent bundles
• Contact 3-manifolds, holomorphic curves and intersection theory
• Stein fillings of contact 3-manifolds obtained as Legendrian surgeries
• Contact structures and reducible surgeries
• Fillings of unit cotangent bundles of nonorientable surfaces
• Generalizations of planar contact manifolds to higher dimensions
• On contact type hypersurfaces in 4-space
• Fillability of small Seifert fibered spaces
• Tight Planar Contact Manifolds with Vanishing Heegaard Floer Contact Invariants
• Stein fillings of homology $3$-spheres and mapping class groups
• On symplectic fillings of virtually overtwisted torus bundles
• 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
• On Legendrian surgeries between lens spaces