The negative slope algorithm and the dimension group of free rank 3
  E. G. Effros and C-L. Shen constructed the dimension group of free rank 2 from the simple continued fraction algorithm. The notion of negative slope algorithm was introduced by S. Ferenczi, C. Holton, and L. Zamboni in their study of 3-interval exchange transformations. The negative slope algorithm is the 2-dimensional continued fraction algorithm. Then the author succeed to construct the dimensional group of free rank 3 by the similar method which E. G. Effros and C-L. Shen used. 
Koshiro Ishimura
math.DS math.GR