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Invariance Theory : The Heat Equation and the Atiyah-Singer Index Theorem - Peter B. Gilkey

Invariance Theory

The Heat Equation and the Atiyah-Singer Index Theorem

By: Peter B. Gilkey

eText | 2 May 2018 | Edition Number 1

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This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used 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. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.

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Non-FictionMathematicsApplied MathematicsEngineering & TechnologyMechanical Engineering & MaterialsMechanical EngineeringEnvironmental ScienceScienceBiology, Life SciencesLife Sciences in GeneralPhysicsApplied Physics
GeometryDifferential & Riemannian GeometryTopologyCalculus & Mathematical AnalysisDifferential Calculus & Equations

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