A combinatorial representation of links by quasitoric braids (Q1348747)

According to Alexander's theorem, every link admits a representation by a closed braid. Markov proved that two braids \(\alpha\) and \(\beta\) represent the same link if and only if \(\alpha\) can be transformed to \(\beta\) by using a sequence of local transformations called Markov moves. In the present paper, the author introduces the notion of quasitoric braids and shows that all link isotopy classes can be encoded by quasitoric braids. It is worth mentioning that quasitoric braids represent a very small class of braids that forms a subgroup of the braid group. This subgroup contains the pure braids.