Ebook: Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem
Author: Gilkey Peter B., Krantz Steven George
- Series: Studies in Advanced Mathematics Ser
- Year: 2018
- Publisher: Chapman and Hall/CRC
- City: Boca Raton
- Edition: 2nd ed
- Language: English
- pdf
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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