A Combinatorial Representation of Links by Quasitoric Braids

To date, many ways for encoding links have been discovered, see, e.g., [1, 5], and [3]. One of them is the encoding by closures of braids (Alexander’s theorem, see, e.g., [6]). Thus, it is important to find a ‘good’ class of braids that encodes all link isotopy types. In the present paper, we prove that all link isotopy classes can be encoded by a very small class of so-called quasitoric braids; this class forms a subgroup in the braid group.