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  3. The Laplacian on a Riemannian Manifold
  • Cited by 334
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    • Publisher:
      Cambridge University Press
      Publication date:
      24 December 2009
      09 January 1997
      ISBN:
      9780511623783
      9780521463003
      9780521468312
      DOI:
      https://doi.org/10.1017/CBO9780511623783
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.393kg, 188 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.286kg, 188 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
      Series:
      London Mathematical Society Student Texts (31)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
    Series:
    London Mathematical Society Student Texts (31)
    Information

    Book description

    This text on analysis of Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The Atiyah-Singer index theorem and its applications are developed (without complete proofs) via the heat equation method. Zeta functions for Laplacians and analytic torsion are also treated, and the recently uncovered relation between index theory and analytic torsion is laid out. The text is aimed at students who have had a first course in differentiable manifolds, and the Riemannian geometry used is developed from the beginning. There are over 100 exercises with hints.

    Reviews

    "The book is well written.... This book provides a very readable introduction to heat kernal methods and it can be strongly recommended for graduate students of mathematics looking for a thorough introduction to the topic." Friedbert PrÜfer, Mathematical Reviews

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