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
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7 Citations
Highly Influential Citations
1
Background Citations
2
Methods Citations
2
Results Citations
1

7 Citations

Citation Type

Citation Type

Virtual Knot Cobordism and Bounding the Slice Genus
TLDR
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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

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Virtual Knot Cobordism and Bounding the Slice Genus
TLDR
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
TLDR
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
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
TLDR
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
TLDR
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…
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