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...

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1. Verfasser: Rosenberg, Steven 1951-
Format: E-Book
Sprache:English
Veröffentlicht: Cambridge Cambridge University Press 1997
Schriftenreihe:London Mathematical Society student texts 31
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520 |a 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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spelling Rosenberg, Steven 1951-
The Laplacian on a Riemannian manifold an introduction to analysis on manifolds Steven Rosenberg
Cambridge Cambridge University Press 1997
1 Online-Ressource (x, 172 Seiten)
txt
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London Mathematical Society student texts 31
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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spellingShingle Rosenberg, Steven 1951-
The Laplacian on a Riemannian manifold an introduction to analysis on manifolds
title The Laplacian on a Riemannian manifold an introduction to analysis on manifolds
title_auth The Laplacian on a Riemannian manifold an introduction to analysis on manifolds
title_exact_search The Laplacian on a Riemannian manifold an introduction to analysis on manifolds
title_full The Laplacian on a Riemannian manifold an introduction to analysis on manifolds Steven Rosenberg
title_fullStr The Laplacian on a Riemannian manifold an introduction to analysis on manifolds Steven Rosenberg
title_full_unstemmed The Laplacian on a Riemannian manifold an introduction to analysis on manifolds Steven Rosenberg
title_short The Laplacian on a Riemannian manifold
title_sort laplacian on a riemannian manifold an introduction to analysis on manifolds
title_sub an introduction to analysis on manifolds
url https://doi.org/10.1017/CBO9780511623783
work_keys_str_mv AT rosenbergsteven thelaplacianonariemannianmanifoldanintroductiontoanalysisonmanifolds
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