Connecting discrete Morse functions via birth-death transitions

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-09-12 DOI:10.1016/j.topol.2025.109594

Chong Zheng

引用次数: 0

Abstract

We study transformations between discrete Morse functions on a finite simplicial complex via birth-death transitions—elementary chain maps between discrete Morse complexes that either create or cancel pairs of critical simplices. We prove that any two discrete Morse functions

f_{1}, f_{2} : K \to R

on a finite simplicial complex K are linked by a finite sequence of such transitions. As applications, we present alternative proofs of several of Forman's fundamental results in discrete Morse theory and study the topology of the space of discrete Morse functions.

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通过出生-死亡转换连接离散莫尔斯函数

我们研究了有限简单复合体上离散莫尔斯函数之间的变换，通过生成或消去临界简单复合体对的离散莫尔斯复合体之间的生-死转换-初等链映射。证明了在有限简单复合体K上任意两个离散莫尔斯函数f1，f2:K→R是由一个有限的这种跃迁序列连接起来的。作为应用，我们给出了Forman在离散莫尔斯理论中的几个基本结果的替代证明，并研究了离散莫尔斯函数空间的拓扑结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.