Homology spheres bounding acyclic smooth manifolds and symplectic fillings

2020/04/16 by John B. Etnyre, Etnyre, John B., Bülent Tosun +1
Mathematics · #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.2004.07405

openalex publication_date 2020/04/16 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

In this paper, we collect various structural results to determine when an integral homology 3--sphere bounds an acyclic smooth 4--manifold, and when this can be upgraded to a Stein manifold. In a different direction we study whether smooth embedding of connected sums of lens spaces in ℂ² can be upgraded to a Stein embedding, and determined that this never happens.

Related

• Stein fillings of homology 3-spheres and mapping class groups
• A note on embeddings of 3-manifolds in symplectic 4-manifolds
• Symplectic rational homology ball fillings of Seifert fibered spaces
• Computability and the growth rate of symplectic homology
• An S² × S² embedding