Index Theorem. 1
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.
Kategorien:
Jahr:
2007
Verlag:
American Mathematical Society
Sprache:
english
Seiten:
205
ISBN 10:
0821820974
ISBN 13:
9780821820971
Serien:
Translations of Mathematical Monographs 235
Datei:
DJVU, 1.81 MB
IPFS:
,
english, 2007