| 中文摘要 | 第1-6页 |
| Abstract | 第6-8页 |
| chapter 1 Introduction | 第8-12页 |
| chapter 2 Spin~c Dirac operators and a mod k localization formula | 第12-24页 |
| ·Spin~c Dirac operators on Z/k manifolds | 第12-16页 |
| ·Z/k circle actions and a variation formula | 第16-17页 |
| ·A mod k localization formula for Z/k circle actions | 第17-21页 |
| ·A Z/k extension of Hattori's vanishing theorem | 第21-24页 |
| chapter 3 A proof of Theorem 2.7 | 第24-38页 |
| ·Witten deformation on flat spaces | 第24-25页 |
| ·A Taylor expansion of certain operators near the fixed-point set | 第25-28页 |
| ·A decomposition of Dirac type operators under consideration and the associated deformation | 第28-31页 |
| ·Various estimates of the operators as T→+∞ | 第31-33页 |
| ·A proof of Theorem 2.7 | 第33-38页 |
| chapter 4 Rigidity and vanishing theorems on Z/k Spin~c manifolds | 第38-50页 |
| ·Rigidity and vanishing theorems | 第38-42页 |
| ·Several intermediate results | 第42-47页 |
| ·A proof of Theorem 4.4 | 第47-50页 |
| chapter 5 A proof of Theorem 4.9 | 第50-64页 |
| ·The refined shift operators | 第50-53页 |
| ·The Spin~c Dirac operators on X(n_j) | 第53-61页 |
| ·A proof of Theorem 4.9 | 第61-64页 |
| Bibliography | 第64-68页 |
| 致谢 | 第68-70页 |
| 个人简历,在学期间发表的学术论文及研究成果 | 第70页 |
