The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds (London Mathematical Society Student Texts Book 31) 1st Edition by Steven Rosenberg (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There was a problem I don’t recall exactly, that the algorithm didn’t work after 1-forms. Perhaps it was related to the definition of inner product defined by the aid of Hodge Star Operator on exterior products, might be related to the alternization of tensor products, not sure!

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