Ordering Thurston's geometries by maps of non-zero degree

31 May 2017 · Neofytidis Christoforos ·

We obtain an ordering of closed aspherical 4-manifolds that carry a non-hyperbolic Thurston geometry. As application, we derive that the Kodaira dimension of geometric 4-manifolds is monotone with respect to the existence of maps of non-zero degree.