All Outputs (3)

Computations of the slice genus of virtual knots (2018)
Journal Article
Rushworth, W. (2019). Computations of the slice genus of virtual knots. Topology and its Applications, 253, 57-84. https://doi.org/10.1016/j.topol.2018.11.028

A virtual knot is an equivalence class of embeddings of $ S^1 $ into thickened (closed oriented) surfaces, up to self-diffeomorphism of the surface and certain handle stabilisations. The slice genus of a virtual knot is defined diagrammatically, in d... Read More about Computations of the slice genus of virtual knots.

Doubled Khovanov Homology (2018)
Journal Article
Rushworth, W. (2018). Doubled Khovanov Homology. Canadian journal of mathematics, 75(5), 1130-1172. https://doi.org/10.4153/CJM-2017-056-6

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 that it can be used to show that some virtual links are non-classical... Read More about Doubled Khovanov Homology.

Additional gradings on generalisations of Khovanov homology and invariants of embedded surfaces (2018)
Journal Article
Olegovich Manturov, V., & Rushworth, W. (2018). Additional gradings on generalisations of Khovanov homology and invariants of embedded surfaces. Journal of Knot Theory and Its Ramifications, 27(9), https://doi.org/10.1142/S0218216518420014

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 kinds of embeddings. These include invariants of links in thickened sur... Read More about Additional gradings on generalisations of Khovanov homology and invariants of embedded surfaces.