1. Geometric structures, Gromov norm and Kodaira dimensions.
- Author
-
Zhang, Weiyi
- Subjects
- *
ALGEBRAIC geometry , *DIMENSIONS , *MANIFOLDS (Mathematics) , *GEOMETRIC analysis , *INVARIANTS (Mathematics) , *MATHEMATICAL mappings - Abstract
We define the Kodaira dimension for 3-dimensional manifolds through Thurston's eight geometries, along with a classification in terms of this Kodaira dimension. We show this is compatible with other existing Kodaira dimensions and the partial order defined by non-zero degree maps. For higher dimensions, we explore the relations of geometric structures and mapping orders with various Kodaira dimensions and other invariants. Especially, we show that a closed geometric 4-manifold has nonvanishing Gromov norm if and only if it has geometry H 2 × H 2 , H 2 ( C ) or H 4 . [ABSTRACT FROM AUTHOR]
- Published
- 2017
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