Combinatorial Garside Structures for Braid Groups

Garside theory has played a central role in solving the word problem and prove famous conjectures for braid groups. In this dissertation, we present Garside theory with particular attention to the recently proposed approach of combinatorial Garside structures, then recover such structures in the symmetric group. We introduce the braid group on n strands, and describe how it arises from the symmetric group through combinatorial Garside structures. As a consequence, the word problem is solved for the braid group and a finite classifying space is explicitly constructed.