On some decompositions of the 3-strand Singular Braid Group

Abstract

Let SB n be the singular braid group generated by braid generators σ i and singular braid generators τ i , 1 ≤ i ≤ n − 1. Let ST n denote the group that is the kernel of the homomorphism that maps, for each i, σ i to the cyclic permutation (i, i + 1) and τ i to 1. In this paper we investigate the group ST 3 . We prove that ST 3 is isomorphic to the pure singular braid group SP 3 on 3 strands.