Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem

Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem

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Book Description
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.

Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem,Peter B. Gilkey,CRC,0849378745,Applied,Atiyah-Singer index theorem,Differential operators,Heat equation,Invariants,Manifolds (Mathematics),Mathematics,Science/Mathematics,Topology,Mathematics / Applied,Mathematics for scientists & engineers,Theoretical methods

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