The geometry of topological stability:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1995
|
| Series: | London Mathematical Society: London Mathematical Society monographs / New series
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | VIII, 572 Seiten Illustrationen |
| ISBN: | 0198535880 9780198535881 |
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Record in the Search Index
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| adam_text | IMAGE 1
THE GEOMETRY OF
TOPOLOGICAL STABILITY
ANDREW DU PLESSIS MATEMATISK INSTITUT, AARHUS UNIVERSITET, DENMARK AND
TERRY WALL DEPARTMENT OF PURE MATHEMATICS, UNIVERSITY OF LIVERPOOL, UK
CLARENDON PRESS * OXFORD
1995
IMAGE 2
CONTENTS
PART I PROLEGOMENA TO STABILITY THEORY 1 GENERAL INTRODUCTION 3
2 REVIEW OF STABILITY THEORY 19
2.1 INTRODUCTION 19
2.2 NOTATION: GERMS, JETS, EQUIVALENCE RELATIONS 20
2.3 (TESTABILITY 25
2.4 FINITE SINGULARITY TYPE 29
2.5 STRATIFICATION THEORY . 32
2.6 C-STABILITY 43
3 PROPER MAPS AND FUNCTION SPACE TOPOLOGIES 49
3.1 INTRODUCTION 49
3.2 TOPOLOGY OF PROPER MAPS 50
3.3 TWO USEFUL LEMMAS V 57
3.4 FUNCTION SPACE TOPOLOGIES 58
3.5 EXISTENCE OF GLOBAL UNFOLDINGS 72
3.6 UNFOLDINGS AND STABILITY 77
3.7 PROOFS OF STABILITY THEOREMS 84
4 VARIOUS NOTIONS OF STABILITY 92
4.1 INTRODUCTION 92
4.2 GLOBAL STABILITY: COMPACT SOURCE 95
4.3 GLOBAL STABILITY: NON-COMPACT SOURCE 100
4.4 LOCAL AND SEMI-GLOBAL STABILITY 111
4.5 THE RELATION BETWEEN GLOBAL AND LOCAL STABILITY 114
IMAGE 3
VI CONTENTS
PART II NECESSARY CONDITIONS
5 DISRUPTIVE GERM CLASSES 121
5.1 INTRODUCTION 121
5.2 GERM CLASSES 122
5.3 LOCAL DEFINITIONS 124
5.4 PERSISTENCE 130
5.5 DISRUPTIVE GERMS 136
5.6 STRONG DISRUPTIVENESS 140
5.7 DISRUPTIVENESS AND INSTABILITY 148
5.8 QUASI-DISRUPTIVE GERMS 152
5.9 FINITE C-DETERMINACY 158
6 NECESSARY CONDITIONS FOR TOPOLOGICAL STABILITY 160
6.1 INTRODUCTION 160
6.2 DIRECT APPLICATION OF RESULTS FROM CHAPTER 5 162
6.3 THE IMMERSION CONDITION 169
6.4 INDUCTIVE CRITERIA FOR ST-INVARIANCE AND DISRUPTIVENESS 177 6.5
QUASI-DISRUPTIVENESS 182
6.6 APPLICATIONS OF QUASI-DISRUPTIVENESS 189
6.7 LST-INVARIANTS AND REGULARITY CONDITIONS J 193
7 STABLE TOPOLOGICAL INVARIANCE OF ^-CONSTANT STRATA 199
7.1 INTRODUCTION 199
7.2 SIMPLE AND UNIMODAL SINGULARITIES 201
7.3 EXCEPTIONAL DEFORMATIONS 209
7.4 TRIPLE AND QUADRUPLE POINTS ,215
7.5 FUNCTIONS OF THREE VARIABLES WITH REDUCED 3-JET 220
7.6 COMPLETE INTERSECTION CURVES 226
7.7 COMPLETE INTERSECTION CUSP SINGULARITIES 240
7.8 COMPLETE INTERSECTION SURFACES 251
8 STABLE TOPOLOGICAL TYPE OF FINITE MAP-GERMS 260
8.1 INTRODUCTION 260
8.2 CODIMENSIONS 263
8.3 Z 2 : FIRST CASES 268
8.4 I 2 - 1 GERMS 273
8.5 I 2 - 2 GERMS OF ORDER 3 283
8.6 GERMS OF I (2 TYPE 291
8.7 GERMS OF I 3(3) TYPE 314
APPENDIX: TABLE OF EQUIDIMENSIONAL STRATA 339
IMAGE 4
CONTENTS VII
PART III SUFFICIENT CONDITIONS
9 A SUFFICIENT CONDITION FOR STRONG TOPOLOGICAL STABILITY 345
9.1 INTRODUCTION 345
9.2 FROM LOCAL TO GLOBAL STABILITY 350
9.3 TAME RETRACTIONS 357
9.4 MULTITRANSVERSALITY IMPLIES TAME P-C-STABILITY 376
9.5 CONSTRUCTING GLOBAL TAME RETRACTIONS FROM LOCAL ONES 379
9.6 CIVILIZATION AND WEIGHTED HOMOGENEITY 386
10 ALGEBRAIC CRITERIA FOR CIVILIZATION 398
10.1 INTRODUCTION 398
10.2 INSTABILITY LOCI 399
10.2.1 STANDARD NOTATIONS 399
10.2.2 RECAPITULATION OF THEOREM 9.6.6 401
10.2.3 EXAMPLE: 7(3, 4) 403
10.2.4 EXAMPLE: THE //-SERIES 404
10.2.5 EXAMPLE: LFV33 406
10.2.6 EXAMPLE: LFT X3 (E = 1) 408
10.3 A CRITERION FOR CIVILIZATION 410
10.3.1 GEOMETRICAL DISCUSSION 410
10.3.2 AN ALGEBRAIC CRITERION FOR CIVILIZATION . 412
10.3.3 TRANSVERSALITY PROPERTIES OF ALMOST-STABLE MAPPINGS 416
10.4 INSTABILITY IDEALS AND DISCRIMINANT MATRICES 421
10.4.1 INSTABILITY IDEALS AND DISCRIMINANT MATRICES 421
10.4.2 AN ALGORITHM FOR DISCRIMINANT MATRICES 424
10.4.3 THE 1-JET OF THE DISCRIMINANT MATRIX AND THE BASIC PAIRING 427
10.4.4 EXAMPLE: 4(2) (GENERIC STRATUM) 431
10.4.5 EXAMPLE: THE STRATUM FA 3 U FC 0 (S = T) 433
10.4.6 REFINEMENTS OF THE ALGORITHM 435
10.4.7 EXAMPLE: LFR 3 3 REVISITED 439
10.4.8 COMPARISON WITH DAMON S ALGORITHM 443
10.5 FURTHER PROPERTIES OF DISCRIMINANT MATRICES 445
10.5.1 CONSEQUENCES OF FINITE SINGULARITY TYPE 445
10.5.2 EXAMPLES: D N+ I , 448
10.5.3 REFINEMENTS OF THE DISCRIMINANT MATRIX 451
10.5.4 POINCARE SERIES 460
10.5.5 EXAMPLE: THE J AND F SERIES 465
10.5.6 SYMMETRY OF THE DISCRIMINANT MATRIX AND THE E-SERIES , 472
IMAGE 5
VIII CONTENTS
10.6 EXTENSIONS 479
10.6.1 GENERAL REMARKS 479
10.6.2 SIMPLIFICATIONS OF THE THEORY 483
10.6.3 EXAMPLES: EXTENSIONS OF THE /,;+2 AND 1(2,1) 485 10.6.4
APPLICATIONS TO /-EXTENSIONS AND 0-EXTENSIONS 488 10.6.5 EXTENSIONS OF
7(3,4) 491
10.6.6 EXTENSIONS OF LFV 3) 3 492
11 CALCULATIONS OF INSTABILITY LOCI 494
11.1 DESCRIPTION OF METHODS OF CALCULATION 494
11.2 INTERPRETATION OF THE DATA 501
11.3 SUMMARY OF CALCULATIONS: HYPERSURFACE CASES S T = 1 503
11.4 SUMMARY OF CALCULATIONS: COMPLETE INTERSECTIONS WITH S T 1 515
11.5 SUMMARY OF CALCULATIONS: THE EQUIDIMENSIONAL CASE S - T 528 11.6
SUMMARY OF CALCULATIONS: CASES S T 534
PART IV CONCLUSION
12 NECESSARY AND SUFFICIENT CONDITIONS FOR STABILITY 543
12.1 INTRODUCTION 543
12.2 STABILITY AND MULTITRANSVERSALITY 543
12.3 THE CASE N P 546
12.4 THE CASE N P 549
12.5 NECESSARY AND SUFFICIENT CONDITIONS FOR STABILITY 552
PROBLEMS 554
REFERENCES 557
INDEX OF TERMINOLOGY 568
|
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| spelling | Du Plessis, Andrew 20. Jht. Verfasser (DE-588)1089209452 aut The geometry of topological stability Andrew du Plessis (Matematisk Institut, Aarhus Universitet, Denmark) and Terry Wall (Department of Pure Mathmematics, University of Liverpool, UK) Oxford Clarendon Press 1995 VIII, 572 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society monographs / New series 9 Hier auch später erschienene, unveränderte Nachdrucke Geometrija Topologija - Diferencialna topologija Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Differentialtopologie (DE-588)4012255-4 gnd rswk-swf Stabile Abbildung (DE-588)4121712-3 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 s Differentialtopologie (DE-588)4012255-4 s DE-604 Stabile Abbildung (DE-588)4121712-3 s Wall, C. T. C. 1936- Verfasser (DE-588)107575256 aut New series London Mathematical Society: London Mathematical Society monographs 9 (DE-604)BV045355493 9 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007022437&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Du Plessis, Andrew 20. Jht Wall, C. T. C. 1936- The geometry of topological stability Geometrija Topologija - Diferencialna topologija Singularität Mathematik (DE-588)4077459-4 gnd Differentialtopologie (DE-588)4012255-4 gnd Stabile Abbildung (DE-588)4121712-3 gnd |
| subject_GND | (DE-588)4077459-4 (DE-588)4012255-4 (DE-588)4121712-3 |
| title | The geometry of topological stability |
| title_auth | The geometry of topological stability |
| title_exact_search | The geometry of topological stability |
| title_full | The geometry of topological stability Andrew du Plessis (Matematisk Institut, Aarhus Universitet, Denmark) and Terry Wall (Department of Pure Mathmematics, University of Liverpool, UK) |
| title_fullStr | The geometry of topological stability Andrew du Plessis (Matematisk Institut, Aarhus Universitet, Denmark) and Terry Wall (Department of Pure Mathmematics, University of Liverpool, UK) |
| title_full_unstemmed | The geometry of topological stability Andrew du Plessis (Matematisk Institut, Aarhus Universitet, Denmark) and Terry Wall (Department of Pure Mathmematics, University of Liverpool, UK) |
| title_short | The geometry of topological stability |
| title_sort | the geometry of topological stability |
| topic | Geometrija Topologija - Diferencialna topologija Singularität Mathematik (DE-588)4077459-4 gnd Differentialtopologie (DE-588)4012255-4 gnd Stabile Abbildung (DE-588)4121712-3 gnd |
| topic_facet | Geometrija Topologija - Diferencialna topologija Singularität Mathematik Differentialtopologie Stabile Abbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007022437&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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