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| 研究生： |
阮登科 Nguyen, Dang Khoa |
|---|---|
| 論文名稱： |
有向圖的路徑餘調與布朗函子 Path cohomology of digraphs as a Brown functor |
| 指導教授： |
廖軒毅
Liao, Hsuan-Yi |
| 口試委員: |
鄭志豪
Teh, Jyh Haur 阮志豪 Yuen, Chi Ho |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2024 |
| 畢業學年度： | 112 |
| 語文別： | 英文 |
| 論文頁數： | 28 |
| 中文關鍵詞： | 布朗表現 、路徑餘調 、有向圖 、代數拓撲 |
| 外文關鍵詞： | Brown Representation, Path Cohomology, Directed Graph, Algebraic Topology |
| 相關次數： | 點閱：26 下載：0 |
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在此篇論文中,我們證明有限定向圖的零階和一階路徑同調群是布朗函子。
In this paper, we prove that the zeroth and first path cohomology groups of a finite directed graph are Brown functors.
References
[1] J. F. Adams. “A variant of E. H. Brown’s representability theorem”. In: Topology 10 (1971), pp. 185–198. doi: 10.1016/0040-9383(71)90003-6.
[2] Alexander Grigor’yan, Yuri Muranov, and Shing-Tung Yau. “On a cohomology of digraphs and Hochschild cohomology”. In: J. Homotopy Relat. Struct. 11.2 (2016), pp. 209–230. doi: 10.1007/s40062-015-0103-1.
[3] Alexander Grigor’yan, Yong Lin, Yuri Muranov, and Shing-Tung Yau. “Cohomology of digraphs and (undirected) graphs”. In: Asian J. Math. 19.5 (2015), pp. 887–931. doi: 10.4310/AJM. 2015.v19.n5.a5.
[4] Alexander Grigor’yan, Yong Lin, Yuri Muranov, and Shing-Tung Yau. “Homologies of path complexes and digraphs”. In: (July 2012). doi: 10.48550/ARXIV.1207.2834. arXiv: 1207.2834 [math.CO].
[5] Alexander Grigor’yan, Yong Lin, Yuri Muranov, and Shing-Tung Yau. “Homotopy theory for digraphs”. In: Pure Appl. Math. Q. 10.4 (2014), pp. 619–674. doi: 10.4310/PAMQ.2014.v10. n4.a2.
[6] Zachary McGuirk and Byungdo Park. “Brown representability for directed graphs”. In: (Mar. 2020). doi: 10.48550/ARXIV.2003.07426. arXiv: 2003.07426 [math.CT].
[7] E. Riehl. Category theory in context. Aurora: Dover modern math originals. Dover Publications, 2017. isbn: 978-0-486-82080-4