Virtual Knots and Links

This paper is an introduction to the subject of virtual knot theory and presents a discussion of some new specific theorems about virtual knots. The new results are as follows: Using a 3-dimensional topology approach, we prove that if a connected sum of two virtual knots $K_1$ and $K_2$ is trivial, then so are both $K_1$ and $K_2$. We establish an algorithm for recognizing virtual links that is based on the Haken–Matveev technique.