Memoirs of The American Mathematical Society Number 22 A Global Formulation of The Lie Theory of TraPDF电子书下载

Chapter Ⅰ．QUOTIENT MANIFOLDS DEFINED BY FOLIATIONS 1

1．Differentiable Manifolds 1

2．Foliations 5

3．The Continuation Theorem 10

4．Regularity 13

5．Quotient Manifolds 19

6．Factorization of Mappings 22

7．Projection-Like Mappings 25

8．The Uniqueness Theorem 28

9．Products of Quotient Manifolds 29

Chapter Ⅱ．LOCAL AND INFINITESIMAL TRANSFORMATION GROUPS 31

1．Notation 32

2．Elementary Definitions 32

3．＇Factoring＇ a Transformation Group 37

4．The Infinitesimal Graph 38

5．The Local Existence Theorem 46

6．The Uniqueness Theorem 49

7．The Existence Theorem 52

Chapter Ⅲ．GLOBALIZABLE INFINITESIMAL TRANSFORMATION GROUPS 59

1．Globalizations 59

2．Univalent Infinitesimal Transformation Groups 62

3．Maximum Local Transformation Groups 65

4．The Principal Theorem 72

5．Proper Infinitesimal Transformation Groups 73

6．Uniform Infinitesimal Transformation Groups 76

7．R-transformation Groups 82

8．The Need for Non-Hausdorff Manifolds 85

9．Can Theorem XX Be Generalized? 87

Chapter Ⅳ．LIE TRANSFORMATION GROUPS 90

1．Two Theorems on Lie Groups 91

2．Infinitesimal Groups 93

3．Connected Lie Transformation Groups 97

4．Lie Transformation Groups 99

5．Tensor Structures and Their Automorphism Groups 106

Appendix to Chapter IV． 112

1．Compact-Open Topology 112

2．Making a Topology Locally Arcwise Connected 112

3．The Modified Compact-Open Topology 114

4．Weakening the Topology of a Lie Group 114

Fixed Notations 120

Terminological Index 121

References 123