**International Press**

Volume: 96;
2013;
792 pp;
Hardcover

MSC: Primary 58; 83;
**Print ISBN: 978-1-57146-264-0
Product Code: INPR/96**

List Price: $95.00

AMS Member Price: $76.00

# Index Theory with Applications to Mathematics and Physics

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*David D. Bleecker; Bernhelm Booß-Bavnbek*

A publication of International Press of Boston

This book describes, explains, and explores the Index Theorem of
Atiyah and Singer, one of the truly great accomplishments of
twentieth-century mathematics whose influence continues to grow, fifty
years after its discovery. The Index Theorem has given birth to many
mathematical research areas and exposed profound connections between
analysis, geometry, topology, algebra, and mathematical
physics. Hardly any topic of modern mathematics stands independent of
its influence.

In this ambitious new work, the authors give two proofs of the
Atiyah–Singer Index Theorem in impressive detail: one based on
\(K\)-theory and the other on the heat kernel approach. As a
preparation for this, the authors explain all the background
information on such diverse topics as Fredholm operators,
pseudo-differential operators, analysis on manifolds, principal
bundles and curvature, and \(K\)-theory carefully and with
concern for the reader. Many applications of the theorem are given, as
well as an account of some of the most important recent developments
in the subject, with emphasis on gauge theoretic physical models and
low-dimensional topology.

The 18 chapters and two appendices of the book introduce different
topics and aspects, often beginning from scratch, without presuming
full knowledge of all the preceding chapters. Learning paths, through
a restricted selection of topics and sections, are suggested and
facilitated. The chapters are written for students of mathematics and
physics: some for the upper-undergraduate level, some for the graduate
level, and some as an inspiration and support for researchers.

Index Theory with Applications to Mathematics and Physics is a
textbook, a reference book, a survey, and much more. Written in a
lively fashion, it contains a wealth of basic examples and
exercises. The authors have included many discussion sections that are
both entertaining and informative and which illuminate the thinking
behind the more general theory. A detailed bibliography and index
facilitate the orientation.

A publication of International Press of Boston. Distributed worldwide by the American Mathematical Society.

#### Readership

Undergraduate and graduate students as well as research mathematicians interested in the Index Theorem of Atiyah–Singer.