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The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds /
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, U.K. ; New York, NY, USA :
Cambridge University Press,
1997.
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| Colección: | London Mathematical Society student texts ;
31. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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. |
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| Descripción Física: | 1 online resource (x, 174 pages) |
| Bibliografía: | Includes bibliographical references (pages 165-169) and index. |
| ISBN: | 9781107362062 1107362067 9780511623783 051162378X 9780511961540 0511961545 |