The Geometry of Topological Stability (London Mathematical Society Monographs)

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 C0-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. The aim of the book is to give necessary and sufficient conditions for a map to be stable. This is achieved in a wide range of dimensions via a detailed study of the geometry and topology of many classes of "generic" singularities.