Index Theorem. 1
Read a fragment
Instant download
after payment (24/7)
Wide range of formats
(for all gadgets)
Full book
(including for Apple and Android)
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.
LF/964228/R
Data sheet
- Name of the Author
- Mikio Furuta
- Language
- English
- Series
- Translations of Mathematical Monographs 235
- ISBN
- 9780821820971
- Release date
- 2007
