Markov's Theorem

Markov's theorem states that equivalent braids expressing the same link are mutually related by successive applications of two types of Markov moves. Markov's theorem is difficult to apply in practice, so it is difficult to establish the equivalence or nonequivalence of links having different braid representations.

REFERENCES:

Markov, A. A. "Über die freie Äquivalenz der geschlossenen Zöpfe." Recueil Math. Moscou 1, 73-78, 1935.

Markov, A. A. "Über die freie Äquivalenz der geschlossenen Zöpfe." Mat. Sbornik 43, 73-78, 1936.

Murasugi, K. and Kurpita, B. I. A Study of Braids. Dordrecht, Netherlands: Kluwer, 1999.