The connectedness homomorphism between discrete Morse complexes

被引：0

作者：

Zheng, Chong ^{[1
]}

机构：

[1] Waseda Univ, Fac Sci & Engn, Shinkuju Ku, Tokyo 1698555, Japan

来源：

TOPOLOGY AND ITS APPLICATIONS | 2024年 / 355卷

关键词：

Discrete Morse theory; Connectedness; Connectedness homomorphism; Birth-death transitions;

D O I：

10.1016/j.topol.2024.109022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by -nc -nd /4 .0/).

引用

页数：18

共 22 条

[1]

Arnol'd V.I., 1998, Singularity theory, VI

[2] Discrete Morse theory on graphs [J].

Ayala, R. ;

Fernandez, L. M. ;

Fernandez-Ternero, D. ;

Vilches, J. A. .

TOPOLOGY AND ITS APPLICATIONS, 2009, 156 (18) :3091-3100

[3]

Benedetti B, 2016, ANN SCUOLA NORM-SCI, V16, P335

[4]

Brueggemann J, 2023, Arxiv, DOI arXiv:2312.14032

[5] A Simplicial Complex is Uniquely Determined by Its Set of Discrete Morse Functions [J].

Capitelli, Nicolas Ariel ;

Minian, Elias Gabriel .

DISCRETE & COMPUTATIONAL GEOMETRY, 2017, 58 (01) :144-157

[6]

Cerf Jean., 1970, Publications Mathematiques de lIHES, V39, P5, DOI 10.1007/BF02684687

[7] Complexes of discrete Morse functions [J].

Chari, MK ;

Joswig, M .

DISCRETE MATHEMATICS, 2005, 302 (1-3) :39-51

[8]

Donovan C, 2023, NEW YORK J MATH, V29, P1393

[9] On the homotopy and strong homotopy type of complexes of discrete Morse functions [J].

Donovan, Connor ;

Lin, Maxwell ;

Scoville, Nicholas A. .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2023, 66 (01) :19-37

[10] Morse theory for cell complexes [J].

Forman, R .

ADVANCES IN MATHEMATICS, 1998, 134 (01) :90-145

← 1 2 3 →