The connectedness homomorphism between discrete Morse complexes

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-07-24 DOI:10.1016/j.topol.2024.109022

Chong Zheng

引用次数: 0

Abstract

Given two discrete Morse functions on a simplicial complex, we introduce the connectedness homomorphism between the corresponding discrete Morse complexes. This concept leads to a novel framework for studying the connectedness in discrete Morse theory at the chain complex level. In particular, we apply it to describe a discrete analogy to ‘cusp-degeneration’ of Morse complexes. A precise comparison between smooth case and our discrete cases is also given.

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离散莫尔斯复合体之间的连通性同态性

给定简单复数上的两个离散莫尔斯函数，我们引入了相应离散莫尔斯复数之间的关系。这一概念为在链复数层面研究离散莫尔斯理论中的连通性提供了一个新框架。特别是，我们应用它来描述莫尔斯复数的离散类比 "尖顶生成"。我们还给出了光滑情况与离散情况之间的精确比较。

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.