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9780198535881

The Geometry of Topological Stability

by ;
  • ISBN13:

    9780198535881

  • ISBN10:

    0198535880

  • Format: Hardcover
  • Copyright: 1996-02-22
  • Publisher: Clarendon Press

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Summary

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.

Table of Contents

Prolegomena to Stability Theory
General Introduction
Review of Stability Theory
Proper Maps and Function Space Topologies
Various Notions of Stability
Necessary Conditions
Disruptive Germ Classes
Necessary Conditions for Topological Stability
Stable Topological Invariance of U-Constant Strata
Stable Topological Type of Finite Map-Germs
Sufficient Conditions
A Sufficient Condition for Strong Topological Stability
Algebraic Criteria for Civilization
Calculations of Instability Loci
Conclusion
Necessary and Sufficient Conditions for Stability
Problems
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

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