The CAT(0) dimension of 3-generator Artin Groups
The three generator Artin groups A(m,n.2) are known to be have CAT(O) dimension strictly greater than two if both m and n are odd [BC]. In Chapter 1 we introduce the notions of CAT(O) dimension and three generator Artin groups. In Chapter 2 we show that if one of m or n is even, then the three generator Artin group has CAT(O) dimension two. In Chapter 3 we extend work by Noel Brady and John Crisp [BC] to enlarge the subclass of groups A(m.n.2) known to have CAT(O) dimension three. In Chapter 4 we classify the structure of a canonical cell complex which the group A(m,n,2) acts on for the case where m is even, greater or equal to six and not divisible by four and n is prime, greater or equal to five. Finally, in Chapter 5 we use the results of Chapter 4 to exhibit classes of rank four Artin groups with CAT(O) dimension two. and a class of rank six Artin groups with CAT(O) dimension two.