论文标题
倍增和常规社区
Hyperbolization and regular neighborhoods
论文作者
论文摘要
我们表明，多面体的倍地化会撤回PL子延伸的常规邻里。将其应用于由Ontaneda引起的Riemannian版本的倍层化，从而提供了打开的捏合负曲率的完整歧管，这些曲率是同质的，相当于闭合的光滑歧管，但没有光滑的刺。我们还发现开放的完整的负面折叠式歧管，这些歧管同等于封闭的非平滑歧管。
We show that the hyperbolization of polyhedra pulls back regular neighborhoods of PL submanifolds. Applying this to the Riemannian version of the hyperbolization due to Ontaneda gives open complete manifolds of pinched negative curvature that are homotopy equivalent to closed smooth manifolds but contain no smooth spines. We also find open complete negatively pinched manifolds that are homotopy equivalent to closed non-smoothable manifolds.
