Geometric structures, Gromov norm and Kodaira dimensions

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Venue:GL 166

Tuesday, March 22, 3:30-4:30pm, GL 166,

Professor Weiyi Zhang, University of Warwick

Title: Geometric structures, Gromov norm and Kodaira dimensions

Abstract: 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.