Geometric structures, Gromov norm and Kodaira dimensions
Geometric structures, Gromov norm and Kodaira dimensions
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DOI：
10.1016/j.aim.2016.12.005
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发表时间：
2014-04
期刊：
影响因子：
--
通讯作者：
Weiyi Zhang
中科院分区：
文献类型：
--
作者：
Weiyi Zhang
我们定义的科代拉维度三维流形通过瑟斯顿的八个几何，沿着分类在这方面的科代拉维度。我们表明，这是兼容与其他现有的科代拉尺寸和非零度地图定义的偏序。对于更高的维度，我们探讨的几何结构和映射顺序与各种科代拉维和其他不变量的关系。特别地，我们证明了闭几何4-流形具有非零Gromov范数当且仅当它具有几何H2 × H2，H2（C）或H4.
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.