Topology and Geometry for Physics

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.

Covers all the important topics of topology and geometry in physics in a very comprehensive way Completely closed presentation of topological concepts for theoretical physics Didactically well written Mathematically strict level A valuable textbook for students of theoretical physics Includes supplementary material: sn.pub/extras

Inhalt
Introduction.- Topology.- Manifolds.- Tensor Fields.- Integration, Homology and Cohomology.- Lie Groups.- Bundles and Connections.- Parallelism, Holonomy, Homotopy and (Co)homology.- Riemannian Geometry.- Compendium.