Prof. Dr. Weiyi Zhang, Warwick Universtity
Geometric structures, Gromov norm and Kodaira dimensions
Kodaira dimension provides a very successful classification scheme for complex manifolds. The notion was extended to symplectic 4-manifolds. In this talk, we will define the Kodaira dimension for 3-manifolds through Thurston's eight geometries. It is compatible with the mapping order and other Kodaira dimensions in the sense of 'additivity'. This idea could be extended to 4-dimensional geometric manifolds. Those with highest Kodaira dimension are distinguished by nonvanishing Gromov norm. Finally, we will see how it is sitting in a potential classification of 4-manifolds.