Stein fillings of planar open books

Abstract

We prove that if a contact manifold $(M,\xi )$ is supported by a planar open book, then Euler characteristic and signature of any Stein filling of $(M,\xi )$ is bounded. We also prove a similar finiteness result for contact manifolds supported by spinal open books with planar pages. Moving beyond the geography of Stein fillings, we classify fillings of some lens spaces.

Minor typos fixed

Cited by in corpus (13)

• On symplectic fillings of spinal open book decompositions I: Geometric constructions
• Positive factorizations of mapping classes
• Stein fillings of contact 3-manifolds obtained as Legendrian surgeries
• Contact surgery on the Hopf link: classification of fillings
• Fillings of unit cotangent bundles of nonorientable surfaces
• Comparing star surgery to rational blow-down
• Partial twists and exotic Stein fillings
• On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification
• Stein fillings of homology $3$-spheres and mapping class groups
• Some applications of Menke's JSJ decomposition for symplectic fillings
• Unexpected Stein fillings, rational surface singularities, and plane curve arrangements
• Symplectic fillings of virtually overtwisted contact structures on lens spaces
• Arbitrarily Long Factorizations in Mapping Class Groups