Alexander duality for functions: the persistent behavior of land and water and shore
Alexander duality for functions: the persistent behavior of land and water and shore
复制标题
函数的亚历山大二元性：土地、水和海岸的持久行为
DOI：
10.1145/2261250.2261287
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Michael Kerber
中科院分区：
文献类型：
--
作者：
H. Edelsbrunner;Michael Kerber
本文通过将亚历山大对偶从空间推广到实值函数，对持久同调的点演算作出了贡献。给定一个完备莫尔斯函数f：Sspacen+1 -> [0，1]和一个分解Sspacen+1 = Uspace <$Vspace为两个具有公共边界Mspace的（n+1）-流形，我们证明了f在Uspace、Vspace和Mspace上的持久图之间的初等关系.
This note contributes to the point calculus of persistent homology by extending Alexander duality from spaces to real-valued functions. Given a perfect Morse function f: Sspacen+1 -> [0,1] and a decomposition Sspacen+1 = Uspace ∪ Vspace into two (n+1)-manifolds with common boundary Mspace, we prove elementary relationships between the persistence diagrams of f restricted to Uspace, to Vspace, and to Mspace.