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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/22742
Title: | Twisted Alexander Polynomial 及其應用 Twisted Alexander Polynomial and Its Applications |
Authors: | Chih-Tai Liu 劉志泰 |
Advisor: | 楊樹文(Su-Win Yang) |
Keyword: | 扭結理論,多項式不變量,纖維扭結, knot,polynomial,invariant,fibered knot, |
Publication Year : | 2010 |
Degree: | 碩士 |
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。 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/22742 |
Fulltext Rights: | 未授權 |
Appears in Collections: | 數學系 |
Files in This Item:
File | Size | Format | |
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ntu-99-1.pdf Restricted Access | 1.01 MB | Adobe PDF |
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