Moduli spaces of morse functions for persistence
Moduli spaces of morse functions for persistence
复制标题
持久性莫尔斯函数的模空间
DOI：
10.1007/s41468-020-00055-x
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Zabka, Matthew
中科院分区：
文献类型：
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作者：
Catanzaro, Michael J.;Curry, Justin M.;Fasy, Brittany Terese;Lazovskis, Jānis;Malen, Greg;Riess, Hans;Wang, Bei;Zabka, Matthew
考虑了球上摩尔斯函数在持久同调条件下的不同等价概念，并引入了新的不变量来研究这些等价类。这些新的不变量与现有的拓扑不变量（如持久性条形码和Reeb图）一样简单，但更具辨识性。在考虑图等价莫尔斯函数的基础上，给出了球上任意两个莫尔斯-小向量场用一系列基本运动联系起来的方法。我们还探讨了高度等效莫尔斯函数的组合丰富世界，将其视为嵌入球的高度函数。他们的水平集不变量，由嵌套磁盘和水平集的环空生成的偏序集，提供了对共享相同持久性条形码的莫尔斯函数的模空间的洞察。
We consider different notions of equivalence for Morse functions on the sphere in the context of persistent homology and introduce new invariants to study these equivalence classes. These new invariants are as simple—but more discerning than—existing topological invariants, such as persistence barcodes and Reeb graphs. We give a method to relate any two Morse–Smale vector fields on the sphere by a sequence of fundamental moves by considering graph-equivalent Morse functions. We also explore the combinatorially rich world of height-equivalent Morse functions, considered as height functions of embedded spheres in. Their level set invariant, a poset generated by nested disks and annuli from level sets, gives insight into the moduli space of Morse functions sharing the same persistence barcode.