分层简单同调类型：理论与计算

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-08-12 DOI:10.1016/j.aam.2024.102753

Markus Banagl , Tim Mäder , Filip Sadlo

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引用次数: 0

摘要

将经典简单同调理论中的基本简单坍缩和展开的思想推广到分层环境中，我们发现了分层简单复合物上的局部组合变换，这些变换使全局分层同调类型保持不变。特别是，我们得到了分层形式变形的概念，概括了怀特海（J. H. C. Whitehead）的形式变形。我们实现了这种变形的算法执行和交点同调的计算，以说明与在给定空间（可能是奇异空间）附近采样的点集相关联的 Vietoris-Rips 型复合物上的分层简单同调等价物的行为。

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Stratified simple homotopy type: Theory and computation

Generalizing the idea of elementary simplicial collapses and expansions in classical simple homotopy theory to a stratified setting, we find local combinatorial transformations on stratified simplicial complexes that leave the global stratified homotopy type invariant. In particular, we obtain the notions of stratified formal deformations generalizing J. H. C. Whitehead's formal deformations. We implement the algorithmic execution of such transformations and the computation of intersection homology to illustrate the behavior of stratified simple homotopy equivalences on Vietoris-Rips type complexes associated to point sets sampled near given, possibly singular, spaces.

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.