SINGULAR BRAIDS AND MARKOVS THEOREM

In this article we will give anew version of Markov's Theorem, treatin g singular braids and knots in the sense of Vassiliev's theory of knot invariants. The classical Version of Markov's Theorem states that two closed braids represent the same link if and only if the braids are r elated by a sequence of algebraic operations, known as Markov's moves. Birman has published the first rigorous proof of this regular version in 1975 [Bir1] using elementary techniques. Our proof uses a suitable version of these techniques in order to reduce the singular case to t he regular case. Birman's proof then completes ours. Some technical po ints will only be sketched. Full details can be found in [Gem].