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数学进展 - 2020, Vol. 49(6): 737-755
研究论文
顶点加权有向图的持续同调
Persistent Homology of Vertex-weighted Digraphs

王冲1, 2, 任世全3, 林勇3
WANG Chong1, 2, REN Shiquan3, LIN Yong3, ***

1. 中国人民大学数学学院, 北京, 100872;
2. 沧州师范学院数学与统计学院, 沧州, 河北, 061000;
3. 清华大学丘成桐数学科学中心, 北京, 100084
1. School of Mathematics, Renmin University of China, Beijing, 100872, P. R. China;
2. School of Mathematics and Statistics, Cangzhou Normal University, Cangzhou, Hebei, 061000, P. R. China;
3. Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, P. R. China

收稿日期: 2020-04-20
出版日期: 2020-11-17
2020, Vol. 49(6): 737-755
DOI: 10.11845/sxjz.2020065b


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摘要 本文回顾了文献[J. Homotopy Relat. Struct., 2016, 11(2): 209-230]中引入的同调, 讨论了权重对持续权重道路同调的影响, 证明了顶点加权有向图连接的库尼斯公式的持续形式.
关键词 有向图权重道路同调持续权重道路同调库尼斯公式    
Abstract:In this paper, we review the homology introduced in [J. Homotopy Relat. Struct., 2016, 11(2): 209-230], discuss the effects of the weights on the persistent weighted path homology and prove a persistent version of the K$\ddot{u}$nneth formula for joins of vertex-weighted digraphs.
Key wordsdigraph    weighted path homology    persistent weighted path homology    K$\ddot{u}$nneth formula
PACS:  O189.22  
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