Topology and geometry for physics
By: Helmut Eschrig
Series: Lecture notes in physics -- v. 822
Publisher: Springer
Published: 2011
Place of publication: Heidelberg; New York
Language: eng
Number of pages: 389
ISBN-13: 9783642146992
Subjects: Differential Geometry; Geometry; Mathematical physics; Topology
Description: 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. --Book Jacket.
Notes: Includes bibliographical references and indexes.
Table of contents: title: Introduction; title: Topology; title: Manifolds; title: Tensor fields; title: Integration, homology and cohomology; title: Lie groups; title: Bundles and connections; title: Parallelism, holonomy, homotopy and (co)homology; title: Riemannian geometry; title: Compendium.