**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

2007; 205 pp; Softcover

MSC: Primary 58;

**Print ISBN: 978-0-8218-2097-1**

Product Code: MMONO/235

Product Code: MMONO/235

List Price: $42.00

Individual Member Price: $33.60

#### Supplemental Materials

# Index Theorem. 1

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*Mikio Furuta*

The Atiyah-Singer index theorem is a remarkable result that allows one to
compute the space of solutions of a linear elliptic partial differential
operator on a manifold in terms of purely topological data related to the
manifold and the symbol of the operator. First proved by Atiyah and Singer
in 1963, it marked the beginning of a completely new direction of research
in mathematics with relations to differential geometry, partial
differential equations, differential topology, K-theory, physics, and
other areas.

The author's main goal in this volume is to give a complete proof of the
index theorem. The version of the proof he chooses to present is the one
based on the localization theorem. The prerequisites include a first
course in differential geometry, some linear algebra, and some facts about
partial differential equations in Euclidean spaces.

#### Readership

Graduate students interested in index theory.

#### Reviews & Endorsements

The book is well organized... The strategy of the proof and applications are clearly laid out. ...this monograph is an important contribution to the subject.

-- Mathematical Reviews