2-Morse函数的分岔和持久路径

IF 0.6 3区数学 Q3 MATHEMATICS

Algebraic and Geometric Topology Pub Date : 2023-09-07 DOI:10.2140/agt.2023.23.2895

Ryan Budney, Tomasz Kaczynski

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引用次数: 6

摘要

对一般光滑函数f: M—> R^2，研究了紧流形的双滤波作为平面滤波的前像的同伦型。本文的主要目标是允许对与此类过滤相关的多分级持久同源性的简单描述。本文的主要结果是描述了f在细胞附着物方面的双重过滤的演变。推导了沿所谓的持续路径的莫尔斯-康利方程和莫尔斯不等式的类比。提出了一种计算路径条形码的方案。

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Bifiltrations and persistence paths for 2–Morse functions

This paper studies the homotopy-type of bi-filtrations of compact manifolds induced as the pre-image of filtrations of the plane for generic smooth functions f : M --> R^2. The primary goal of the paper is to allow for a simple description of the multi-graded persistent homology associated to such filtrations. The main result of the paper is a description of the evolution of the bi-filtration of f in terms of cellular attachments. An analogy of Morse-Conley equation and Morse inequalities along so called persistence paths are derived. A scheme for computing path-wise barcodes is proposed.

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来源期刊

Algebraic and Geometric Topology 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebraic and Geometric Topology is a fully refereed journal covering all of topology, broadly understood.