4 papers
Even and odd Kauffman bracket ideals for genus-1 tangles
Susan M. Abernathy, Patrick M. Gilmer
This paper refines previous work by the first author. We study the question of which links in the 3-sphere can be obtained as closures of a given 1-manifold in an unknotted solid t…
The Kauffman bracket ideal for genus-1 tangles
Susan M. Abernathy
Given a compact oriented 3-manifold M in S^3 with boundary, an (M,2n)-tangle T is a 1-manifold with 2n boundary components properly embedded in M. We say that T embeds in a link L…
On Krebes' tangle
Susan M. Abernathy
A genus-1 tangle G is an arc properly embedded in a standardly embedded solid torus S in the 3-sphere. We say that a genus-1 tangle embeds in a knot K in S^3 if the tangle can be c…
A reduced set of moves on one-vertex ribbon graphs coming from links
Susan Abernathy, Cody Armond, Moshe Cohen +5
Every link in R^3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.