All Outputs (3)

Ascent concordance (2021)
Journal Article
Rushworth, W. (2021). Ascent concordance. Algebraic and Geometric Topology, 21(6), 3073–3106. https://doi.org/10.2140/agt.2021.21.3073

A cobordism between links in thickened surfaces consists of a surface $ S $ and a $3$-manifold $M $, with $ S $ properly embedded in $ M \times I $. We show that there exist links in thickened surfaces such that if $(S,M) $ is a cobordism between the... Read More about Ascent concordance.

A parity for 2-colourable links (2021)
Journal Article
Rushworth, W. (2021). A parity for 2-colourable links. Osaka Journal of Mathematics, 58(4), 767–801

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 certain type of colouring. The 2-colour parity is an extension of the Gauss... Read More about A parity for 2-colourable links.

Minimal crossing number implies minimal supporting genus (2021)
Journal Article
Boden, H., & Rushworth, W. (2021). Minimal crossing number implies minimal supporting genus. Bulletin of the London Mathematical Society, 53(4), 1174-1184. https://doi.org/10.1112/blms.12491

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 virtual link diagram has minimal genus across representatives of the st... Read More about Minimal crossing number implies minimal supporting genus.