Abstract

This paper is an introduction to the subject of virtual knot theory, combined with a discussion of some specific new theorems about virtual knots. The new results are as follows: We prove, using a 3-dimensional topology approach that if a connected sum of two virtual knots K1 and K2 is trivial, then so are both K1 and K2. We establish an algorithm, using Haken-Matveev technique, for recognizing virtual knots. This paper may be read as both an introduction and as a research paper. For more about Haken-Matveev theory and its application to classical knot theory, see [Ha, Hem, Mat, HL]. 1

Citations