Stein fillings of planar open books

2013/11/01 by Amey Kaloti, Kaloti, Amey · 2 citations
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Logic, programming, and type systems #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1311.0208

openalex publication_date 2013/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if a contact manifold (M,ξ) is supported by a planar open book, then Euler characteristic and signature of any Stein filling of (M,ξ) 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.

Cited by

• On symplectic fillings of spinal open book decompositions II:\n Holomorphic curves and classification
• Stein fillings of homology 3-spheres and mapping class groups
• Arbitrarily Long Factorizations in Mapping Class Groups
• Stein fillings of contact 3-manifolds obtained as Legendrian surgeries

Related

• A note on Mazur type Stein fillings of planar contact manifolds
• Families of contact 3-manifolds with arbitrarily large Stein fillings
• Planar contact 3-manifolds with infinitely many Stein fillings
• Stein-fillability and positivity in the mapping class group
• Contact 5-manifolds admitting open books with exotic pages