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.

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