In presenting a detailed study of the geometry and topology of numerous classes of "generic" singularities, Geometry of Topological Stability bridges the gap between algebraic calculations and continuity arguments to detail the necessary and sufficient conditions for a C (infinity) to be C]0-stable. Throughout, the authors masterfully examine this important subject using results culled from a broad range of mathematical disciplines, including geometric topology, stratification theory, algebraic geometry, and commutative algebra. Packed with original research, much of which is presented here for the first time, the book will be welcomed by students and researchers interested in singularity theory and related areas.

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

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