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

Peter B. Gilkey

出版	Publish or Perish, 1984
主題	Mathematics / Differential Equations / GeneralMathematics / Transformations
ISBN	09140982099780914098201
URL	http://books.google.com.hk/books?id=JW_vAAAAMAAJ&hl=&source=gbs_api

註釋

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, & 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.