# Computations of the slice genus of virtual knots

@article{Rushworth2019ComputationsOT,
title={Computations of the slice genus of virtual knots},
author={William Arthur Rushworth},
journal={Topology and its Applications},
year={2019}
}
• W. Rushworth
• Published 26 June 2017
• Mathematics
• Topology and its Applications
Virtual Knot Cobordism and Bounding the Slice Genus
• Computer Science
Exp. Math.
• 2019
The graded genus of Turaev's graded genus is remarkably effective as a slice obstruction, and an algorithm is developed that applies virtual unknotting operations to determine the slice genus of many virtual knots with six or fewer crossings.
Virtual concordance and the generalized Alexander polynomial
• Mathematics
• 2019
We use the Bar-Natan Zh-correspondence to identify the generalized Alexander polynomial of a virtual knot with the Alexander polynomial of a two component welded link. We show that the Zh-map is
Signature and concordance of virtual knots
• Mathematics
• 2017
We introduce signature invariants of virtual knots and use them to investigate virtual knot concordance. The signatures, which depend on a choice of Seifert surface, are defined first for almost
Virtual knot homology and concordance
We construct and investigate the properties of a new extension of Khovanov homology to virtual links, known as doubled Khovanov homology. We describe a perturbation of doubled Khovanov homology,
Virtual Seifert surfaces
A virtual knot that has a homologically trivial representative [Formula: see text] in a thickened surface [Formula: see text] is said to be an almost classical (AC) knot. [Formula: see text] then
Doubled Khovanov Homology
Abstract 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
Milnor's concordance invariants for knots on surfaces
Milnor's $\bar{\mu}$-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

## References

SHOWING 1-10 OF 31 REFERENCES
Virtual Knot Cobordism and Bounding the Slice Genus
• Computer Science
Exp. Math.
• 2019
The graded genus of Turaev's graded genus is remarkably effective as a slice obstruction, and an algorithm is developed that applies virtual unknotting operations to determine the slice genus of many virtual knots with six or fewer crossings.
A self-linking invariant of virtual knots
A new invariant of virtual knots and links that is non-trivial for many virtuals, but is trivial on classical knots and Links is introduced, which is an interpretation of the state sum in terms of 2-colorings of the associated diagrams.
Khovanov Homology, Lee Homology and a Rasmussen Invariant for Virtual Knots
• Mathematics
• 2014
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 cobordisms which directly
STABLE EQUIVALENCE OF KNOTS ON SURFACES AND VIRTUAL KNOT COBORDISMS
• Mathematics, Computer Science
• 2000
An equivalence relation, called stable equivalence, is introduced on knot diagrams and closed generically immersed curves on surfaces and it is shown that Kauffman's example of a virtual knot diagram is not equivalent to a classical knot diagram.
Doubled Khovanov Homology
Abstract 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
Virtual Knot Cobordism
This paper defines a theory of cobordism for virtual knots and studies this theory for standard and rotational virtual knots and links. Non-trivial examples of virtual slice knots are given.
A Sequence of Degree One Vassiliev Invariants for Virtual Knots
For ordinary knots in R3, there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of
Parity and Cobordisms of Free Knots
In the present paper, we construct a simple invariant which provides a sliceness obstruction for {\em free knots}. This obstruction provides a new point of view to the problem of studying cobordisms
ABSTRACT LINK DIAGRAMS AND VIRTUAL KNOTS
• Computer Science
• 2000
It is prove that there is a bijection from the equivalence classes of virtual link diagrams to those of abstract link diagrams, and a generalization to higher dimensional cases is introduced, and the state-sum invariants are treated.
The Rasmussen invariant of a homogeneous knot
A homogeneous knot is a generalization of alternating knots and positive knots. We determine the Rasmussen invariant of a homogeneous knot. This is a new class of knots such that the Rasmussen