By Steven Rosenberg

ISBN-10: 0521468310

ISBN-13: 9780521468312

This article on research on Riemannian manifolds is an intensive advent to themes coated in complex examine monographs on Atiyah-Singer index concept. the most subject is the learn of warmth circulation linked to the Laplacians on differential kinds. this gives a unified remedy of Hodge idea and the supersymmetric evidence of the Chern-Gauss-Bonnet theorem. specifically, there's a cautious therapy of the warmth kernel for the Laplacian on features. the writer develops the Atiyah-Singer index theorem and its purposes (without whole proofs) through the warmth equation strategy. Rosenberg additionally treats zeta features for Laplacians and analytic torsion, and lays out the lately exposed relation among index conception and analytic torsion. The textual content is aimed toward scholars who've had a primary path in differentiable manifolds, and the writer develops the Riemannian geometry used from the start. There are over a hundred routines with tricks.