The Topological Classification Of Stratified Spaces

This book provides the theory for stratified spaces along with importantexamples and applications that is analogous to the surgery theory formanifolds. In the f... » 

This book provides the theory for stratified spaces along with importantexamples and applications that is analogous to the surgery theory formanifolds. In the first expository account of this field Weinberger providestopologists with a new way of looking at the classification theory of singularspaces with his original results.Divided into three parts the book begins with an overview of modern highdimensional manifold theory. Rather than including complete proofs of alltheorems Weinberger demonstrates key constructions gives convenientformulations and shows the usefulness of the technology. Part II offers theparallel theory for stratified spaces. Here the topological category is mostcompletely developed using the methods of controlled topology. Many examplesillustrating the topological invariance and noninvariance of obstructions andcharacteristic classes are provided. Applications for embeddings and immersionsof manifolds for the geometry of group actions for algebraic varieties andfor rigidity theorems are found in Part III.This volume will be of interest to topologists as well as mathematicians inother fields such as differential geometry operator theory and algebraicgeometry. «