PREFACE

This book deals with a localization approach to the index problem for elliptic operators. Localization ideas for many years have been widely used for solving various specific index problems, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of new important problems in index theory. So far, the general localization principle has been only scarcely covered in journal papers and not covered at all in monographs. The present book is intended to fill the gap. We explain the general localization principle and illustrate it by examples. The book is intended for working mathematicians as well as graduate and postgraduate university students specializing in differential equations and related topics.