2014/07/20 by Takahiro Oba, Oba, Takahiro
Mathematics · #57R17 #57R65 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1407.5257
openalex publication_date 2014/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, using combinatorial techniques of mapping class groups, we show that a Stein fillable integral homology 3-sphere supported by an open book decomposition with page a 4-holed sphere admits a unique Stein filling up to diffeomorphism. Furthermore, according to a property of deforming symplectic fillings of a rational homology 3-spheres into strongly symplectic fillings, we also show that a symplectically fillable integral homology 3-sphere supported by an open book decomposition with page a 4-holed sphere admits a unique symplectic filling up to diffeomorphism and blow-up.