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Informationen zum Autor Gilkey, Peter B. Klappentext Treats the Atiyah-Singer index theorem using the heat equation! which gives a local formula for the index of any elliptic complex. This work also uses heat equation methods to discuss Lefschetz fixed point formulas! the Gauss-Bonnet theorem for a manifold with smooth boundary! and the geometrical theorem for a manifold with smooth boundary. Zusammenfassung This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex Inhaltsverzeichnis Pseudo-Differential OperatorsIntroductionFourier Transform and Sobolev SpacesPseudo-Differential Operators on RmPseudo-Differential Operators on ManifoldsIndex of Fredholm OperatorsElliptic ComplexesSpectral TheoryThe Heat EquationLocal Index FormulaVariational FormulasLefschetz Fixed Point TheoremsThe Zeta FunctionThe Eta FunctionCharacteristic ClassesIntroductionCharacteristic Classes of Complex BundlesCharacteristic Classes of Real BundlesComplex Projective SpaceInvariance TheoryThe Gauss-Bonnet TheoremInvariance Theory and Pontrjagin ClassesGauss-Bonnet for Manifolds with BoundaryBoundary Characteristic ClassesSinger's QuestionThe Index TheoremIntroductionClifford ModulesHirzebruch Signature FormulaSpinorsThe Spin ComplexThe Riemann-Roch TheoremK-TheoryThe Atiyah-Singer Index TheoremThe Regularity at s = 0 of the Eta FunctionLefschetz Fixed Point FormulasIndex Theorem for Manifolds with BoundaryThe Eta Invariant of Locally Flat BundlesSpectral GeometryIntroductionOperators of Laplace TypeIsospectral ManifoldsNon-Minimal OperatorsOperators of Dirac TypeManifolds with BoundaryOther Asymptotic FormulasThe Eta Invariant of Spherical Space FormsA Guide to the LiteratureAcknowledgmentIntroductionBibliographyNotation
