The Geometry of Topological Stability

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.