Virtual Knots and Infinite-Dimensional Lie Algebras

@article{Manturov2004VirtualKA,
  title={Virtual Knots and Infinite-Dimensional Lie Algebras},
  author={V. O. Manturov},
  journal={Acta Applicandae Mathematicae},
  year={2004},
  volume={83},
  pages={221-233}
}
  • V. Manturov
  • Published 1 September 2004
  • Mathematics
  • Acta Applicandae Mathematicae
In the present work, we construct an invariant of virtual knots valued in (infinite-dimensional) Lie Algebras and establish some properties of it. This leads to some heuristic ideas how to construct quandles and extract (virtual) link invariants. 
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References

SHOWING 1-10 OF 11 REFERENCES
On Invariants of Virtual Links
TLDR
The knot quandle, the knot fundamental group, the Alexander module, and the coloring invariants are generalized, which leads to a new method of generalizing classical link invariants for the case of virtual links.
Long virtual knots and their invariants
There are some phenomena arising in the virtual knot theory which are not the case for classical knots. One of them deals with the "breaking" procedure of knots and obtaining long knots. Unlike the
Virtual Knot Theory
This paper is an introduction to the theory of virtual knots. It is dedicated to the memory of Francois Jaeger.
Virtual Knot Groups
Virtual knots, defined by Kauffman, provide a natural generalization of classical knots. Most invariants of knots extend in a natural way to give invariants of virtual knots. In this paper we study
Cocycle knot invariants from quandle modules and generalized quandle homology
Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Grana. We specialize that theory to the case when there is a
The Knot Book
Are you looking to uncover the knot book Digitalbook. Correct here it is possible to locate as well as download the knot book Book. We've got ebooks for every single topic the knot book accessible
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