請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/22742完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 楊樹文(Su-Win Yang) | |
| dc.contributor.author | Chih-Tai Liu | en |
| dc.contributor.author | 劉志泰 | zh_TW |
| dc.date.accessioned | 2021-06-08T04:26:33Z | - |
| dc.date.copyright | 2010-03-11 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-02-12 | |
| dc.identifier.citation | [1] T. Kitano, Twisted Alexander polynomial and Reidemeister torsion, Pacific J. Math. 174 (1996), no. 2, 431-442.
[2] X. S. Lin, Representations of knot groups and twisted Alexander polynomials, Acta Math. Sin. (Engl. Ser.) 17, no. 3: 361-380 (2001) [3] H. Goda, T. Kitano, T. Morifuji, Reidemeister torsion, twisted Alexander polynomial and fibered knots, e-print:math.GT/0311155; Comment. Math. Helv. 80 (2005), no. 1, 51-61. [4] W.B. R. Lickorish, An introduction to knot theory, Springer GTM (1997). [5] V. G. Turaev, Introduction to Combinatorial Torsions, Birkhauser Verlag (2000). [6] M. Wada, Twisted Alexander polynomial for finitely presentable groups, Topology 33 (1994), 241-256. [7] F.Waldhausen, Algebraic K-theory of generalized free products. I, II, Ann. of Math. (2) 108, (1978), 135-204. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/22742 | - |
| dc.description.abstract | 本論文旨在介紹扭結理論中的一個不變量，即Twisted Alexander 多項式。後者乃是利用群表現理論去推廣早期的Alexander多項式。理論上，此不變量與Torsion理論有重要的關聯；而在應用上，除了能辨別更多的扭結之外，我們還得到了一個關於纖維扭結(fibered knot)的必要條件。 | zh_TW |
| dc.description.abstract | In this thesis, we shall introduce an invariant in knot theory, the twisted Alexander polynomial. This generalizes the classical Alexander polynomial, with the help of group representation. Theoretically, this invariant is related with the torsion theory. As for applications, besides that it recognizes much more knots, we shall alsohave a necessary condition for bered knots. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T04:26:33Z (GMT). No. of bitstreams: 1 ntu-99-R96221029-1.pdf: 1032207 bytes, checksum: bd49fbc2af6164e2e84925cfb4491f69 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 英文摘要 iii
第一節 Introduction 1第二節 Twisted Alexander Polynomials 2 第三節 Examples 8 第四節 Twisted Alexander Polynomials as Torsions 13 第五節 Twisted Alexander Polynomials and Fibered Knots 19 第六節 A non-Fibered Knot 21 參考文獻 23 | |
| dc.language.iso | en | |
| dc.subject | 纖維扭結 | zh_TW |
| dc.subject | 多項式不變量 | zh_TW |
| dc.subject | 扭結理論 | zh_TW |
| dc.subject | fibered knot | en |
| dc.subject | knot | en |
| dc.subject | polynomial | en |
| dc.subject | invariant | en |
| dc.title | Twisted Alexander Polynomial 及其應用 | zh_TW |
| dc.title | Twisted Alexander Polynomial and Its Applications | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 翁秉仁(Ping-Zen Ong),王藹農(Ai-Nung Wang) | |
| dc.subject.keyword | 扭結理論,多項式不變量,纖維扭結, | zh_TW |
| dc.subject.keyword | knot,polynomial,invariant,fibered knot, | en |
| dc.relation.page | 23 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2010-02-12 | |
| 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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