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Free eBooks > Science > History & Philosophy > History of Science > Invariance Theory, The Heat Equation, And The Atiyah-singer Index Theorem

Invariance Theory, The Heat Equation, And The Atiyah-singer Index Theorem

by Peter B. Gilkey

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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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