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研究生:蘇 爽
研究生(外文):Su, Shuang
論文名稱:一個從含有單一關係元之有限生成群到SL(2,C)的同態空間之光滑性質的充分條件
論文名稱(外文):A sufficient condition of smoothness of homomorphism space of a finitely generated group with one relator to SL(2,C)
指導教授:何南國
指導教授(外文):Ho, Nan-Kuo
口試委員:吳思曄蕭欽玉
口試委員(外文):Wu, SiyeHsiao, Chin-Yu
口試日期:2021-01-18
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2021
畢業學年度:109
語文別:英文
論文頁數:31
中文關鍵詞:表現簇特徵簇模空間
外文關鍵詞:Representation varietyCharacter varietyModuli space
相關次數:
  • 被引用被引用:0
  • 點閱點閱:221
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  • 下載下載:7
  • 收藏至我的研究室書目清單書目收藏:0
在這篇論文裡,我們嘗試描述從有限循環群到SL(2, C)的同態空間並證明了在這個同態空間中,幾乎所有點都是光滑的。更精確來說,至多只會有兩個孤立奇異點。我們也考慮了一個更一般的情形,從含有單一關係元之有限生成群到SL(2, C)的同態空間。我們找出一個在此同態空間上的光滑性的充分條件。
In this Thesis, we describe the space of homomorphisms from a finite cyclic group to SL(2, C) and show that almost all it’s points are smooth points. More precisely, there are at most two isolated singular points. We also consider a more general case, the homomorphism space of a finitely generated group with a single relator to SL(2, C). We give a sufficient condition of the smoothness of the homomorphism space.
1 Introduction . . . . . . . . . . . .5
2 The homomorphism space . . . . . . . . . . . .6
3 The Fox derivation. . . . . . . . . . . . 8
4 Lyndon's simple identity theorem . . . . . . . . . . . .11
5 The homomorphism space from Z_p to SL(2,C) . . . . . . . . . . . .14
5.1 Description of Hom(\Pi,G) . . . . . . . . . . . . 14
5.2 Lyndon's sequence of \Pi . . . . . . . . . . . . 18
5.3 Calculation of ker(\tensor*[^3]{\check{M}}{^2}) . . . . . . . . . . . . 20
5.4 Calculation of dimH^2(\Pi,\mathfrak{g}_{Ad \circ
hi}) . . . . . . . . . . . . 21
5.5 The main theorem . . . . . . . . . . . . 22
6 Homomorphism space of group with a single relator to SL(2,C) . . . . . . . . . . . . 26
7 Appendix . . . . . . . . . . . . 28
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