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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Cambridge
Cambridge University Press
1997
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Schriftenreihe: | London Mathematical Society student texts
31 |
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100 | 1 | |a Rosenberg, Steven |d 1951- | |
245 | 1 | 4 | |a The Laplacian on a Riemannian manifold |b an introduction to analysis on manifolds |c Steven Rosenberg |
264 | 1 | |a Cambridge |b Cambridge University Press |c 1997 | |
300 | |a 1 Online-Ressource (x, 172 Seiten) | ||
336 | |b txt | ||
337 | |b c | ||
338 | |b cr | ||
490 | 1 | |a London Mathematical Society student texts |v 31 | |
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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id | ZDB-20-CTM-CR9780511623783 |
illustrated | Not Illustrated |
indexdate | 2024-12-18T12:04:30Z |
institution | BVB |
isbn | 9780511623783 |
language | English |
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series2 | London Mathematical Society student texts |
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 c cr 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. Erscheint auch als Druck-Ausgabe 9780521463003 Erscheint auch als Druck-Ausgabe 9780521468312 TUM01 ZDB-20-CTM TUM_PDA_CTM https://doi.org/10.1017/CBO9780511623783 Volltext |
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 AT rosenbergsteven laplacianonariemannianmanifoldanintroductiontoanalysisonmanifolds |