8 citations · 31 across the 11 of their papers we have counts for
12 papers
Some link homologies in
William Rushworth
We introduce extensions of Khovanov homology and the Lee and Bar-Natan spectral sequences for links in . These extensions are distinct to those previously defined…
On knots that divide ribbon knotted surfaces
Hans U. Boden, Ceyhun Elmacioglu, Anshul Guha +4
We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a…
Minimal crossing number implies minimal supporting genus
Hans U. Boden, William Rushworth
A virtual link may be defined as an equivalence class of diagrams, or alternatively as a stable equivalence class of links in thickened surfaces. We prove that a minimal crossing v…
On ribbon graphs and virtual links
Scott Baldridge, Louis H. Kauffman, William Rushworth
We introduce a new equivalence relation on decorated ribbon graphs, and show that its equivalence classes directly correspond to virtual links. We demonstrate how this corresponden…
Generalized Fishburn numbers and torus knots
Colin Bijaoui, Hans U. Boden, Beckham Myers +4
Andrews and Sellers recently initiated the study of arithmetic properties of Fishburn numbers. In this paper, we prove prime power congruences for generalized Fishburn numbers. The…
Ascent concordance
William Rushworth
A cobordism between links in thickened surfaces consists of a surface and a -manifold , with properly embedded in . We show that there exist links…
A parity for 2-colourable links
William Rushworth
We introduce the 2-colour parity. It is a theory of parity for a large class of virtual links, defined using the interaction between orientations of the link components and a certa…
Ascent sliceness
William Rushworth
We introduce the notion of ascent sliceness of virtual knots. A representative of a virtual knot is an embedding , for a closed connec…
Additional gradings on generalisations of Khovanov homology and invariants of embedded surfaces
Vassily Olegovich Manturov, William Rushworth
We define additional gradings on two generalisations of Khovanov homology (one due to the first author, the other due to the second), and use them to define invariants of various k…
Computations of the slice genus of virtual knots
William Rushworth
A virtual knot is an equivalence class of embeddings of into thickened (closed oriented) surfaces, up to self-diffeomorphism of the surface and certain handle stabilisation…
Doubled Khovanov Homology
William Rushworth
We define a homology theory of virtual links built out of the direct sum of the standard Khovanov complex with itself, motivating the name doubled Khovanov homology. We demonstrate…
On the virtual Rasmussen invariant
William Rushworth
We produce chain-level generators of the virtual Lee complex and use them to convert the computable bounds on the Rasmussen invariant of classical knots due to Kawamu…