Lecture Notes in Physics

Eschrig, Helmut

A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation.

Details

Published by: Springer

Publication Date: 2011-02-09

Format: Paperback

ISBN-13: 9783642146992

DOI: 10.1007/978-3-642-14700-5

Dimensions: 235cm x155cm

Pages: 390