A new proof of Markov's braid theorem
The purpose of this paper is to introduce a new proof of Markov's braid theorem, in terms of Seifert circles and Reidemeister moves. This means that the proof will be of combinatorial and essentially 2-dimensional nature. One characteristic feature of our approach is that nowhere in the proof will we use or refer to the braid axis. This allows for greater flexibility in various transformations of the diagrams considered. Other proofs of Markov's theorem can be found in , ,  and .