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Topology and Analysis: The Atiyah-Singer Index Formula and Gauge-Theoretic Physics (Universitext)
Rok: 1984
ISBN: 9780387961125
NKP-CNB: boa001-muni.000387699
OKCZID: 110377451
Citace (dle ČSN ISO 690):
BLEECKER, David. Topology and analysis: the Atiyah-Singer index formula and gauge-theoretic physics. Překlad A. MADER. New York: Springer, c1985. xvi, 451 s. Universitext.
Anotace
The Atiyah-Singer Index Formula is a deep and important result of mathematics which is known for its difficulty as well as for its applicability to a number of seemingly disparate subjects. This book is the first attempt to render this work more accessible to beginners in the field. It begins with the study of the neccessary topics in functional analysis and analysis on manifolds, and is as self-contained as possible. The third part presents the index formula and three proofs; the cobordism proof, the imbedding proof, and the heat equations proof. A section is included which surveys some of the many applications of the index formula, among them the theorem of Riemann-Roch-Hirzebruch. For this first English edition, a chapter on the applications of the Atiyah-Singer Index Formula to gauge theory has been added. This chapter also contains a discussion of Donaldson's theorem.