Invariance Theory

The Heat Equation and the Atiyah-Singer Index Theorem

Nonfiction, Science & Nature, Mathematics, Applied, Technology, Engineering, Mechanical, Science, Physics, General Physics
Cover of the book Invariance Theory by Peter B. Gilkey, CRC Press
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Author: Peter B. Gilkey ISBN: 9781351436427
Publisher: CRC Press Publication: May 2, 2018
Imprint: CRC Press Language: English
Author: Peter B. Gilkey
ISBN: 9781351436427
Publisher: CRC Press
Publication: May 2, 2018
Imprint: CRC Press
Language: English

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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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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