Grupos de tranças virtuais singulares

Abstract

In this work, we present a study on some properties of the group VSGn, which represents virtual singular braids for n ≥ 2. We define numerical invariants for the virtual singular braids, obtained through word exponents in VSGn, and describe the kernel of these homomorphisms. We identify all possible homomorphisms from the group VSGn to the symmetric group Sn, up to conjugation. In the particular case where n = 2, we present a description and a presentation for the kernel in each case. For all possible homomorphisms, decompositions of VSGn were obtained as semi-direct products of the kernel of the homomorphism and the symmetric group.