论文标题
六个manifolds上几乎复杂的结构的拓扑
Topology of Almost Complex Structures on Six-Manifolds
论文作者
论文摘要
我们研究了（正交）几乎复杂的结构在封闭的六维流形上的空间，作为给定度量的曲折空间部分的空间。对于连接的六个manifold和第一个betti的消失，我们表达了几乎复杂的结构的空间，作为通过圆圈动作在歧管上的七个球形束空间的商的商品，然后使用此描述来计算理性同型理论最小模型的组件的模型，以满足某些Chern数字条件。我们进一步获得了曲折空间的两个部分的同源交集的公式，该公式根据相应的几乎复杂结构的Chern类别。
We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with vanishing first Betti number, we express the space of almost complex structures as a quotient of the space of sections of a seven-sphere bundle over the manifold by a circle action, and then use this description to compute the rational homotopy theoretic minimal model of the components that satisfy a certain Chern number condition. We further obtain a formula for the homological intersection number of two sections of the twistor space in terms of the Chern classes of the corresponding almost complex structures.
