《Memoirs of The American Mathematical Society Number 22 A Global Formulation of The Lie Theory of Tra》

Chapter Ⅰ．QUOTIENT MANIFOLDS DEFINED BY FOLIATIONS1

1．Differentiable Manifolds1

2．Foliations5

3．The Continuation Theorem10

4．Regularity13

5．Quotient Manifolds19

6．Factorization of Mappings22

7．Projection-Like Mappings25

8．The Uniqueness Theorem28

9．Products of Quotient Manifolds29

Chapter Ⅱ．LOCAL AND INFINITESIMAL TRANSFORMATION GROUPS31

1．Notation32

2．Elementary Definitions32

3．＇Factoring＇ a Transformation Group37

4．The Infinitesimal Graph38

5．The Local Existence Theorem46

6．The Uniqueness Theorem49

7．The Existence Theorem52

Chapter Ⅲ．GLOBALIZABLE INFINITESIMAL TRANSFORMATION GROUPS59

1．Globalizations59

2．Univalent Infinitesimal Transformation Groups62

3．Maximum Local Transformation Groups65

4．The Principal Theorem72

5．Proper Infinitesimal Transformation Groups73

6．Uniform Infinitesimal Transformation Groups76

7．R-transformation Groups82

8．The Need for Non-Hausdorff Manifolds85

9．Can Theorem XX Be Generalized?87

Chapter Ⅳ．LIE TRANSFORMATION GROUPS90

1．Two Theorems on Lie Groups91

2．Infinitesimal Groups93

3．Connected Lie Transformation Groups97

4．Lie Transformation Groups99

5．Tensor Structures and Their Automorphism Groups106

Appendix to Chapter IV．112

1．Compact-Open Topology112

2．Making a Topology Locally Arcwise Connected112

3．The Modified Compact-Open Topology114

4．Weakening the Topology of a Lie Group114

Fixed Notations120

Terminological Index121

References123