Link Download ebook Free: https://ouo.io/agLpjP The Laplacian on a Riemannian Manifold An Introduction to Analysis on Manifolds By: Steven Rosenberg Publisher: Cambridge University Press Print ISBN: 9780521463003, 0521463009 eText ISBN: 9780511885709, 0511885709 Edition: 1st Format: PDF Available from $ 52.00 USD SKU 9780511885709 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.
