2 papers
math.GT2026
Surface slices and homology spheres
Clayton McDonald
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…
math.GT2025
Constructing knots with low rational genera
Clayton McDonald, Allison N. Miller
We give a flexible construction for knots in the 3-sphere that bound surfaces of unexpectedly low genus in punctured open books on 3-manifolds. We use this construction to give the…