In this paper we construct new invariants of knotoids including the odd writhe, the parity
bracket polynomial, the affine index polynomial and the arrow polynomial, and give an …

We define a group-valued invariant of virtual knots and relate it to various other group-
valued invariants of virtual knots, including the extended group of Silver-Williams and the …

LinKnot? Knot Theory by Computer provides a unique view of selected topics in knot theory
suitable for students, research mathematicians, and readers with backgrounds in other exact …

The goal of this paper is to tabulate all genus one prime virtual knots having diagrams with≤
5 classical crossings. First, we construct all nonlocal prime knots in the thickened torus T× I …

Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string
down to long-chain molecules. The existence of knotting in a filament naturally affects its …

We study concordance of virtual knots. Our main result is that a classical knot $ K $ is
virtually slice if and only if it is classically slice. From this we deduce that the concordance …

In this paper, we compute the slice genus for many low-crossing virtual knots. For instance,
we show that 1295 out of 92,800 virtual knots with six or fewer crossings are slice, and that …

Milnor's μ–invariants of links in the 3–sphere S 3 vanish on any link concordant to a
boundary link. In particular, they are trivial on any knot in S 3. Here we consider knots in …

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 …

We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual
links, using the fact that the theory of virtual links can be translated into the theory of links …