Commutator subgroups of some generalized braid groups

Abstract

Commutator subgroups of Artin’s braid groups B n are well studied by Gorin and Lin in their 1969 paper, where they obtained finite presentation for B n 0 for each n. Later, in 1993, Savushkina gave a simpler presentation for B n 0 . The goal of this thesis is to understand the structure of the commutator subgroups of some of the generalizations of Artin’s braid groups B n , namely the welded braid groups W B n , the generalized virtual braid groups GV B n , the flat welded braid groups F W B n , the flat virtual braid groups F V B n , and the twin groups T W n . As consequences of the above investigations we prove several algebraic and geometric properties of the above groups.