Download PDF by Steven Rosenberg: The Laplacian on a Riemannian Manifold: An Introduction to

By Steven Rosenberg

ISBN-10: 0521463009

ISBN-13: 9780521463003

ISBN-10: 0521468310

ISBN-13: 9780521468312

this article on research of Riemannian manifolds is a radical advent to issues coated in complex examine monographs on Atiyah-Singer index concept. the most subject is the learn of warmth move linked to the Laplacians on differential types. this offers a unified therapy of Hodge idea and the supersymmetric evidence of the Chern-Gauss-Bonnet theorem. specifically, there's a cautious remedy of the warmth kernel for the Laplacian on services. The Atiyah-Singer index theorem and its functions are built (without whole proofs) through the warmth equation procedure. Zeta services for Laplacians and analytic torsion also are taken care of, and the lately exposed relation among index thought and analytic torsion is laid out. The textual content is geared toward scholars who've had a primary path in differentiable manifolds, and the Riemannian geometry used is constructed from the start. There are over a hundred workouts with hints.

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