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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TLDR
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Milnor's concordance invariants for knots on surfaces
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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
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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.
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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
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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
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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.
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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
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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.
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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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