Surface slices and homology spheres
Abstract
We develop the theory of the diagrammatics of surface cross sections to prove that there are an infinite number of homology 3-spheres smoothly embeddable in a homology 4-sphere but not in a homotopy 4-sphere. Our primary obstruction comes from work of Taubes.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Geometric and Algebraic Topology
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Geometry & Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 30
- Issue
- 5
- Pages
- 1611–1623
- Publication date
- 18 July 2026
- Language
- EN