The Geometry of Topological Stability

Hardcover | April 30, 1999

byAndrew A. du Plessis, Terry Wall

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The intention of this book is to give the necessary and sufficient conditions for a C map to be C stable, this objective being achieved in a wide range of dimensions via a detailed study of the geometry and topology of many classes of generic singularities. The methods developed for examining this topology and geometry use results from many areas of mathematics - geometric topology, stratification theory, algebraic geometry, and commutative algebra amoung them, and further progress will doubtless arise from the application of deeper results from theseareas. Conversely, it is to be hoped that they will have interesting consequences for these areas of mathematics, which are those with most interaction with singularity theory. The book describes original research; virtually none of its results have previously appeared elsewhere, either in scientific articles or in books.

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The intention of this book is to give the necessary and sufficient conditions for a C map to be C stable, this objective being achieved in a wide range of dimensions via a detailed study of the geometry and topology of many classes of generic singularities. The methods developed for examining this topology and geometry use results from...

Andrew A. du Plessis, Mathematics Institute, Aarhus University. Terry Wall, Department of Pure Mathematics, University of Liverpool.
Format:HardcoverDimensions:580 pages, 9.21 × 6.14 × 0.01 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198535880

ISBN - 13:9780198535881

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Table of Contents

Part I: Prolegomena to Stability TheoryGeneral introduction1. Review of stability theory2. Proper maps and function space topologies3. Various notions of stabilityPart II: Necessary Conditions4. Disruptive germ classes5. Necessary conditions for topological stability6. Stable topological invariance of u-constant strata7. Stable topological type of finite map-germsPart III: Sufficient Conditions8. A sufficient condition for strong topological stability9. Algebraic criteria for civilization10. Calculations of instability lociPart IV: Conclusion11. Necessary and sufficient conditions for stabilityProblemsReferencesIndex

Editorial Reviews

`In judging the importance of the present work in the context of stability of smooth maps, it cannot be easily overestimated. It guides the reader through a maze of complicated new results including proofs at the center of manifold theory.'Zentralblatt fuer Mathematik 870/97