Virtual knot theory is an extension of classical knot theory to stabilized embeddings of circles
into thickened orientable surfaces of genus possibly greater than zero. Classical knot theory …

The paper contains an essentially self-contained treatment of Khovanov homology,
Khovanov–Lee homology as well as the Rasmussen invariant for virtual knots and virtual …

" Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics.
This enyclopedia is filled with valuable information on a rich and fascinating subject."–Ed …

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 …

Circuit algebras, introduced by Bar-Natan and the first author, are a generalization of
Jones's planar algebras, in which one drops the planarity condition on “connection …

Circuit algebras, used in the study of finite-type knot invariants, are a symmetric analogue of
Jones's planar algebras. They are very closely related to circuit operads, which are a …

We define a second Steenrod square for virtual links, which is stronger than Khovanov
homology for virtual links, toward constructing Khovanov-Lipshitz-Sarkar stable homotopy …

The Jones polynomial and Khovanov homology of a classical link are invariants that depend
upon an initial choice of orientation for the link. In this paper, we give a Khovanov homology …

We define a family of Khovanov-Lipshitz-Sarkar stable homotopy types for the homotopical
Khovanov homology of links in thickened surfaces indexed by moduli space systems. This …

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 …