Two-dimensional Artin groups with CAT(0) dimension three
  We exhibit 3-generator Artin groups which have finite 2-dimensional Eilenberg-Mac Lane spaces, but which do not act properly discontinuously by semi-simple isometries on a 2-dimensional CAT(0) complex. We prove that infinitely many of these groups are the fundamental groups of compact, non-positively curved 3-complexes. These examples show that the geometric dimension of a CAT(0) group may be strictly less than its CAT(0) dimension. 
Noel Brady (University of Oklahoma, Norman), John Crisp (University of   Bourgogne, Dijon)