Presentations of graph braid groups
Daniel Scott Farley, Lucas Sabalka · Forum Mathematicum · 2010
Abstract. Let be a graph. The (unlabeled) configuration space of n points on is the space of n -element subsets of . The n -strand braid group of , denoted , is the fundamental group of . This paper applies the methods of discrete Morse theory to the spaces . We describe how to compute presentations for , where n is an arbitrary natural number and is an arbitrary finite connected graph. Particular attention is paid to the case , and many examples are given.