7 citations · 8 across the 4 of their papers we have counts for
5 papers · 1 filter
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…
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…
Doubly slice Montesinos links
Duncan McCoy, Clayton McDonald
This paper compares notions of double sliceness for links. The main result is to show that a large family of 2-component Montesinos links are not strongly doubly slice despite bein…
Doubly slice odd pretzel knots
Clayton McDonald
We prove that an odd pretzel knot is doubly slice if it has twist parameters consisting of copies of and copies of for some odd integer . Combined with…
Band Number and the Double Slice Genus
Clayton McDonald
We study the double slice genus of a knot, a natural generalization of slice genus. We define a notion called band number, a natural generalization of band unknotting number, and p…