Figure 20: (a) The shear deformation of a torus generates a (projective) non-Abelian geometric phase , which is a generator of a projective representation modular transformation. The last shear-deformed torus is the same as the original torus after a coordinate transformation: , . (b) The squeezing deformation of a torus generates a (projective) non-Abelian geometric phase , which is the other generator of a projective representation modular transformation. The last squeeze-deformed torus is the same as the original torus after a coordinate transformation: , .