請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/18579完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王藹農 | |
| dc.contributor.author | Chang-Han Chueh | en |
| dc.contributor.author | 闕昌漢 | zh_TW |
| dc.date.accessioned | 2021-06-08T01:12:52Z | - |
| dc.date.copyright | 2014-08-17 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-08-14 | |
| dc.identifier.citation | [1] Su-win Yang, Homology Theory of Framed Graphs, National Taiwan University,
2006. [2] Alexander Grigoryan, Yong Lin, Yuri Muranov, and Shing-Tung Yau, Homologies of path complexes and digraphs, Math arXiv: 1207.2834v4 (2013). [3] Alexander Grigoryan, Yuri Muranov, and Shing-Tung Yau, Graphs associated with simplicial complexes, Homology, Homotopy, and Applications 16 (2014), 295311. [4] James W. Vick, Homology Theory : An Introduction to Algebraic Topology, Second Edition, New York : Springer-Verlag, 1994. [5] Allen Hatcher, Algebraic Topology, Cambridge University Press, 2002. [6] Jacob Fox, http://math.mit.edu/~fox/MAT307-lecture03.pdf [7] 張鎮華、蔡牧村，圖論及其演算法, 2011. [8] Chen, Beifang, Yau, Shing-Tung, and Yeh, Yeong-Nan, Graph homotopy and Graham homotopy, Discrete Math., 241 (2001) 153-170. [9] Alexander Grigoryan, Yuri Muranov, Shing-Tung Yau, Cohomology theories of simplicial complexes, algebras, and digraphs, preprint 2012. [10] Alexander Grigoryan, Yuri Muranov, Yong Lin, Shing-Tung Yau, Homotopy theory for digraphs, Math arXiv: 1407.0234v1 (2014). [11] Ching-Hsiang Yu, The Homology Theory of Graphs and The Con guration Space Integral , phd dissertation, National Taiwan University, 2001. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/18579 | - |
| dc.description.abstract | 這篇論文主要是整理[2]、[3]和[10]的結果，介紹定義在路徑上的同調群此一觀念，並討論它在有向圖上的一些應用，最後以此方法重新證明Brouwer’s fixed point theorem。 | zh_TW |
| dc.description.abstract | The main content of this thesis is a reorganization of [2], [3], and [10]. We introduce the notion of path homology and discuss some applications on digraphs; finally we use the method to prove Brouwer’s fixed point theorem in an alternative way. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T01:12:52Z (GMT). No. of bitstreams: 1 ntu-103-R95221030-1.pdf: 548664 bytes, checksum: 04ec86d0e4626304a39bd429e68bc477 (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | Contents
1 Introduction 1 2 Basic definitions and properties 1 2.1 Preliminary. . . . . . . . . . . . . . . . . . . . . 1 2.2 Subspaces to develop the homologies of path complexes . . . . . 3 2.3 The relation between path complexes, simplicial complexes and digraphs . 7 2.4 Form and exterior differential . . . . . . . . . . . . . . . 10 2.5 ∂-invariant paths on digraphs . . . . . . . . . . . . . . . 14 2.6 Homologies of subgraphs. . . . . . . . . . . . . . . . 19 3 Sperner’s lemma and Brouwer’s fixed point theorem 26 3.1 Sperner’s lemma . . . . . . . . . . . . . . . . . . . 26 3.2 Brouwer’s fixed point theorem . . . . . . . . . . . . . . . 28 References 28 | |
| dc.language.iso | en | |
| dc.title | 路徑的同調群 | zh_TW |
| dc.title | Homologies of Path Complexes | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 張海潮,葉永南 | |
| dc.subject.keyword | 路徑,同調,有向圖, | zh_TW |
| dc.subject.keyword | path,homology,digraph, | en |
| dc.relation.page | 29 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2014-08-15 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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| ntu-103-1.pdf 未授權公開取用 | 535.8 kB | Adobe PDF |
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