This book provides the theory for stratified spaces, along with
important examples and applications, that is analogous to the surgery
theory for manifolds. In the first expository account of this field,
Weinberger provides topologists with a new way of looking at the
classification theory of singular spaces with his original results.
Divided into three parts, the book begins with an overview of modern
high-dimensional manifold theory. Rather than including complete proofs
of all theorems, Weinberger demonstrates key constructions, gives
convenient formulations, and shows the usefulness of the technology.
Part II offers the parallel theory for stratified spaces. Here, the
topological category is most completely developed using the methods of
controlled topology. Many examples illustrating the topological
invariance and noninvariance of obstructions and characteristic classes
are provided. Applications for embeddings and immersions of manifolds,
for the geometry of group actions, for algebraic varieties, and for
rigidity theorems are found in Part III.
This volume will be of interest to topologists, as well as
mathematicians in other fields such as differential geometry, operator
theory, and algebraic geometry.