Discrete Morse theory on digraphs

被引：0

作者：

Lin, Yong ^{[1
,2
]}

Wang, Chong ^{[3
,4
]}

Yau, Shing-Tung ^{[5
]}

机构：

[1] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

[2] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China

[3] Cangzhou Normal Univ, Dept Math & Stat, Cangzhou 061000, Hebei, Peoples R China

[4] Renmin Univ China, Sch Math, Beijing 100872, Peoples R China

[5] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

来源：

PURE AND APPLIED MATHEMATICS QUARTERLY | 2021年 / 17卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Discrete Morse theory; quasi-isomorphism; path homology; COHOMOLOGY; HOMOLOGY;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we give a necessary and sufficient condition that discrete Morse functions on a digraph can be extended to be Morse functions on its transitive closure, from this we can extend the Morse theory to digraphs by using quasi-isomorphism between path complex and discrete Morse complex, we also prove a general sufficient condition for digraphs that the Morse functions satisfying this necessary and sufficient condition.

引用

页码：1711 / 1737

页数：27

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