Surface slices and homology spheres
Geometric Topology
2026-01-16 v3
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.
Cite
@article{arxiv.2202.02696,
title = {Surface slices and homology spheres},
author = {Clayton McDonald},
journal= {arXiv preprint arXiv:2202.02696},
year = {2026}
}
Comments
13 pages, 10 figures, clarity improved, an extra hyperbolic geometry argument added at the end to prove that the infinite family of manifolds I produce has infinitely many distinct manifolds in it