• Part I: Prolegomena to Stability Theory


• General introduction


• 1: Review of stability theory


• 2: Proper maps and function space topologies


• 3: Various notions of stability


• Part II: Necessary Conditions


• 4: Disruptive germ classes


• 5: Necessary conditions for topological stability


• 6: Stable topological invariance of u-constant strata


• 7: Stable topological type of finite map-germs


• Part III: Sufficient Conditions


• 8: A sufficient condition for strong topological stability


• 9: Algebraic criteria for civilization


• 10: Calculations of instability loci


• Part IV: Conclusion


• 11: Necessary and sufficient conditions for stability


• Problems


• References


• Index

The aim of this book is to give necessary and sufficient conditions for aCToo map to be CTo-stable: the aim is achieved in a wide range of dimensions via a detailed study of the geometry and topology of many classes of "generic" singularities. Written by internationally renowned authors, the book describes original research, virtually none of which has appeared before in either articles or in book form. The methods developed will stimulate future progress from their application, especially with regard to singularity theory.