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The Laplacian on a Riemanni...
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
Monografía
monografia Rebiun25106864 https://catalogo.rebiun.org/rebiun/record/Rebiun25106864 m|||||o||d|||||||| cr|||||||||||| 090916s1997||||enk o ||1 0|eng|d 9780511623783 ebook) 9780521463003 hardback) 9780521468312 paperback) UkCbUP eng rda UkCbUP 516.3/73 20 Rosenberg, Steven 1951-) author The Laplacian on a Riemannian manifold an introduction to analysis on manifolds Steven Rosenberg Cambridge Cambridge University Press 1997 Cambridge Cambridge Cambridge University Press 1 online resource (x, 172 pages) digital, PDF file(s) 1 online resource (x, 172 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society student texts 31 EBA Cambridge University Press Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 Riemannian manifolds Laplacian operator Print version 9780521463003 London Mathematical Society student texts 31