论文标题
局部到全球Urysohn宽度估计值
Local-to-global Urysohn width estimates
论文作者
论文摘要
Urysohn $ d $ width的概念在多大程度上可以通过$ d $维的简单综合体近似。我们调查了局部乌里索恩（Urysohn）在里曼尼（Riemannian）歧管上的宽度界限如何影响其全球宽度。我们从第一个同源性和单位球的至上宽度上限制了Riemannian歧管的$ 1 $宽度。回答拉里·古斯（Larry Guth）的问题，我们举例说明了$ n $ - manifolds的$（n-1）$ - 宽度，其中所有单位球都有任意的$ 1 $宽度。我们还举例说明了拓扑简单的歧管，这些歧管在局部几乎差不多。
The notion of the Urysohn $d$-width measures to what extent a metric space can be approximated by a $d$-dimensional simplicial complex. We investigate how local Urysohn width bounds on a riemannian manifold affect its global width. We bound the $1$-width of a Riemannian manifold in terms of its first homology and the supremal width of its unit balls. Answering a question of Larry Guth, we give examples of $n$-manifolds of considerable $(n-1)$-width in which all unit balls have arbitrarily small $1$-width. We also give examples of topologically simple manifolds that are locally nearly low-dimensional.
