Stable Equivalence of Knots on Surfaces and Virtual Knot Cobordisms

Details Stable Equivalence of Knots on Surfaces and Virtual Knot Cobordisms Stable Equivalence of Knots on Surfaces and Virtual Knot Cobordisms

2000-08-16

arxiv.org/abs/math/0008118v1

Mathematics

Geometric Topology

12 pages, 9 figures

Scientific paper

We introduce an equivalence relation, called stable equivalence, on knot diagrams and closed curves on surfaces. We give bijections between the set of abstract knots, the set of virtual knots, and the set of the stable equivalence classes of knot diagrams on surfaces. Using these bijections, we define concordance and link homology for virtual links. As an application, it is shown that Kauffman's example of a virtual knot diagram is not equivalent to a classical knot diagram.

Affiliated with

Also associated with

No associations

Rating

Stable Equivalence of Knots on Surfaces and Virtual Knot Cobordisms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stable Equivalence of Knots on Surfaces and Virtual Knot Cobordisms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stable Equivalence of Knots on Surfaces and Virtual Knot Cobordisms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-674151