Singular Points of Smooth Mappings (Research Notes in Mathematics Series)

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Dedication......Page 4
Contents......Page 6
Introduction......Page 8
Acknowledgements......Page 14
1. A Preliminary Review of Some Calculus......Page 15
2. Smooth Manifolds......Page 19
3. The Differential of a Smooth Mapping......Page 23
4. Vector Fields and Flows......Page 31
5. Germs of Smooth Mappings......Page 40
1. The Notion of Transversality......Page 45
2. The Basic Transversality Lemma......Page 55
3, An Elementary Transversality Theorem......Page 58
4. Thom's Transversality Theorem......Page 60
5. First Order Singularity Sets......Page 61
1. Groups Acting on Sets......Page 68
2. Some Geometry of Jets......Page 69
3. Smooth Actions of Lie Groups on Smooth Manifolds......Page 80
4. Transversal Unfoldings......Page 88
5. Versal Unfoldings......Page 96
1. Some Basic Geometric Ideas......Page 101
2. The Algebra......Page 106
3. Determinacy of Germs......Page 123
4. Classification of Germs of Codimension =< 5......Page 129
1. The Basic Ideas......Page 146
2. Contact Equivalence......Page 150
3. Deformations under.'-Equivalence......Page 166
4. Classification of Stable Germs......Page 175
5. Higher Order Singularity Sets......Page 181
6. Classifying Germs under,11-Equivalence......Page 198
7. Some Examples of Classifying Stable Germs......Page 206
8. Singular Points of Stable Mappings......Page 212
Appendix A - The Theorem of Sara......Page 222
Appendix B - Semialgebraic Group Actions......Page 229
Appendix C - Real Algebras......Page 233
Appendix D - The Borel Lemma......Page 235
Appendix E - Guide to Further Reading......Page 239
Index......Page 244