Articles liés à LMSST: 31 Laplacian on Riemannian

LMSST: 31 Laplacian on Riemannian - Couverture souple

Livre 25 sur 83: London Mathematical Society Student Texts

Rosenberg

 
9780521468312: LMSST: 31 Laplacian on Riemannian
Couverture souple
ISBN 10 : 0521468310 ISBN 13 : 9780521468312
Editeur : Cambridge University Press, 2008

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Revue de presse

"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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2008
Langue
anglais
ISBN 10 
0521468310
ISBN 13 
9780521468312
Reliure
Broché
Nombre de pages
188
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

chemin des peupliers 27
Dardilly
France