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

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CRC Press, Dec 22, 1994 - Mathematics - 536 pages
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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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Contents

Characteristic classes
121
The index theorem
215
Spectral geometry
327
Bibliographic information
419
Notation
509
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