The Atiyah-Patodi-Singer Index Theorem

Richard Melrose ISBN 1-56881-002-4

AK Peters - 1993 Hardcover 392pp $59.95

An extended and polished version of a set of lecture notes that was the basis of a course at MIT, this text places the A-P-S index theorem in an analytic framework analogous to that provided by the theory of pseudodifferential operators for the A-S theorem. Here, the A-P-S theorem is used as a pivot to discuss some important aspects of geometry and analysis on manifolds with boundary. MelroseUs straightforward approach is to immediately "state and prove" the theorem and then use the subsequent chapters to flesh out these initial concepts. He goes on to provide a comprehensive introduction to the TbU category and the related calculus of b-pseudodifferential operators on boundaried compact manifolds. This sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.