請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10086完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 楊樹文(Su-Win Yang),李瑩英(Yng-Ing Lee) | |
| dc.contributor.author | Yi-Sheng Wang | en |
| dc.contributor.author | 王以晟 | zh_TW |
| dc.date.accessioned | 2021-05-20T21:00:54Z | - |
| dc.date.available | 2011-07-29 | |
| dc.date.available | 2021-05-20T21:00:54Z | - |
| dc.date.copyright | 2011-07-29 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-07-20 | |
| dc.identifier.citation | [1] D. Bar-Natan, Khovanov's homology for tangles and cobordisms, Geometry and Topology 9 (2005) 1443-1499.
[2] D. Bar-Natan, On Khovanov's categorification of the Jones polynomial, Algebraic and Geometric Topology 2-16 (2002) 337-370. [3] J.S. Carter,M. Saito, Knotted surface and their diagrams, Mathmatical Surveys and Monographs 55, American Mathmatical Society, Providence 1998. [4] L.H. Kauffman, State models and the Jones polynomial, Topology 26-3 (1987) 395-407. [5] J.W. Milnor, Morse theory, Princeton: Princeton University Press,1963. [6] M.Khovanov, A categorification of the Jones polynomial, arXiv:math.QA/9908171. [7] M.Khovanov, A functor-valued invariant of tangles, Alg. Geom. Top. 2 (2002). 665-741,arXiv:math.QA/0103190. [8] M.Khovanov, An invariant of tangle cobordisms, University of California at Davis preprint, Jannuary 2002, arXiv:math.QA/0207264. [9] E. S. Lee, On Khovanov invariant for alternating links, MIT preprint, August 2003, Arxiv:math.GT/0210213. [10] D. Rolfsen, Knots and Links, Publish or Perish Inc., Berkeley, Calif., 1976. Mathematics Lecture Series, No. 7. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10086 | - |
| dc.description.abstract | 在 Khovanov's theory 中，利用結的平滑化， 得到了一個chain complex, 更進一步的可以得到一個結的不變量，稱它為Khovanov's homology。
但在 Bar-Natan 教授的一篇文章中，曾用另一個方式重新解釋這個chain complex，他先不將每一個平滑化的圖，看作向量空間，反而用cobordism作為它的 differential。這是一個更抽象的chain complex,但很特別。這似乎是從一個更原始的角度來看此種chain complex。 本文描述了我們將這個方法推廣到曲面嵌入四維空間(2-knots)的一些結果及遇到的困難，其中也包括如何平滑化曲面圖和一些在 Roseman moves 間的 chain homotopy equivalence。 | zh_TW |
| dc.description.abstract | The Khovanov's homology is the most powerful knot invariant up to now. In [1], Prof. Bar-Natan gives a new idea to interpret the Khovanov's homology. We wonder whether we can mimic his method and apply to the 2-dimensional knots. In this article, we present some results we found, and some difficulties we encountered. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T21:00:54Z (GMT). No. of bitstreams: 1 ntu-100-R98221043-1.pdf: 3068616 bytes, checksum: 0f21aa0f1658f12f008eb66050d1c71d (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 1.Introduction................................. .p.1
2.1-dimensional case.............................p.2 3.Some basic definitions in 2-knots.............p.18 4.Smooth 2-knot diagrams and Cob^{4}............p.23 5.Homotopy equivalences between Roseman moves...p.34 | |
| dc.language.iso | en | |
| dc.title | 二維結的平滑化 | zh_TW |
| dc.title | Smoothings of Knot Diagrams for 2-dimensional Knots | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.advisor-orcid | ,李瑩英(yilee@math.ntu.edu.tw) | |
| dc.contributor.oralexamcommittee | 王藹農(Ai-Nung Wang) | |
| dc.subject.keyword | 結的不變量,二維結,二維結的平滑化, | zh_TW |
| dc.subject.keyword | knot invariant,2-knots,smoothings of 2-knot diagrams, | en |
| dc.relation.page | 47 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2011-07-20 | |
| 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 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-100-1.pdf | 3 MB | Adobe PDF | 檢視/開啟 |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。