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Invariance Theory
Peter B. Gilkey
其他書名
The Heat Equation and the Atiyah-Singer Index Theorem
出版CRC Press, 2018-05-02
主題Mathematics / AppliedTechnology & Engineering / MechanicalScience / Physics / General
ISBN13514364229781351436427
URLhttp://books.google.com.hk/books?id=al1ZDwAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
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, 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.