Invariance Theory, the Heat Equation and the Atiyah-Singer Index Theorem

出版者:CRC-Press

作者:Peter B. Gilkey

页数:536

出版时间:1995-02-01

价格:USD 120.95

装帧:Hardcover

isbn号码:9780849378744

图书标签:数学微分几何指标定理Math热方程几何this微分几何7

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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这本书才是一本真正学术化的指标定理。外尔的渐进公式。分析指标：霍奇定理-热方程-椭圆算子的指标-Lefschetz数-theta函数关系