论文标题
选择性撕裂复合物的有限重建
Finite reconstruction with selective Rips complexes
论文作者
论文摘要
与一系列参数相对应的选择性撕裂络合物是利用薄薄的概念的越野 - 撕-RIPS络合物的概括。我们证明，如果公制空间$ y $接近（Gromov-Hausdorff距离）到封闭的Riemannian歧管$ x $，则可以选择$ y $的选择性撕裂综合体，以达到$ x $的同型。该结果是对Latchev重建的概括是由越野河 - rips络合物引起的选择性撕裂络合物。特别是，我们为Latschev定理提供了一个新颖的证明，作为一种特殊情况。我们还提出了一个功能设置，即使在越野式搭配的情况下，它也是新的。
Selective Rips complexes corresponding to a sequence of parameters are a generalization of Vietoris-Rips complexes utilizing the idea of thin simplices. We prove that if a metric space $Y$ is close (in Gromov-Hausdorff distance) to a closed Riemannian manifold $X$, then selective Rips complexes of $Y$ for certain parameters attain the homotopy type of $X$. This result is a generalization of Latchev's reconstruction result from Vietoris-Rips complexes to selective Rips complexes. In particular, we present a novel proof for the Latschev's theorem as a special case. We also present a functorial setting, which is new even in the case of Vietoris-Rips complexes.
