Introduction

Abstract

The main subject of this book is the index locality principle, which can more precisely be called the superposition principle for the relative index. This introduction, which is partly based on the paper [60] by Nazaikinskii and Sternin, is intended as an elementary introduction to this principle. We discuss it and give some examples of its consequences and applications showing that it often proves to be a powerful tool for obtaining index formulas in various situations. Here we try to keep things as clear as possible and often give only the simplest versions of the results. A more detailed exposition, as well as the proofs, is given in subsequent chapters. Readers are also encouraged to consult the bibliographical remarks at the end of the introduction, which in particular recommend some further reading.