臺灣博碩士論文加值系統

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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