Ordering Thurston's geometries by maps of non-zero degree
arXiv:1607.03058 · doi:10.1142/S1793525318500280
Abstract
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.
18 pages; v2: new section added (Section 6 on Kodaira dimension); v3: minor edits; part of this paper was formerly contained in arXiv:1507.07778; to appear in Journal of Topology and Analysis