论文标题
在平滑的空间中的时间级和因果同型路径类别的分类和拓扑结构上
On the categorical and topological structure of timelike and causal homotopy classes of paths in smooth spacetimes
论文作者
论文摘要
对于平稳的时空$ x $，基于其及时途径的及时同型类别，我们定义了$ x $的拓扑结构，该拓扑结合了$ x $，可以完善Alexandrov拓扑结构，并且始终与歧管拓扑结合在一起。 定时或因果同型类的空间分别形成半酸性或类别。我们表明，这些代数结构中的任何一个都编码足够的信息来重建$ x $的拓扑结构和保形结构。此外，及时同型类的空间具有自然拓扑，我们被证明是本地欧几里得的，但通常不是Hausdorff。 提出的结果不需要$ x $上的任何因果条件，也需要在较弱的规律性假设下保持。
For a smooth spacetime $X$, based on the timelike homotopy classes of its timelike paths, we define a topology on $X$ that refines the Alexandrov topology and always coincides with the manifold topology. The space of timelike or causal homotopy classes forms a semicategory or a category, respectively. We show that either of these algebraic structures encodes enough information to reconstruct the topology and conformal structure of $X$. Furthermore, the space of timelike homotopy classes carries a natural topology that we prove to be locally euclidean but, in general, not Hausdorff. The presented results do not require any causality conditions on $X$ and do also hold under weaker regularity assumptions.
