By Helmut Eschrig

A concise yet self-contained creation of the valuable strategies of recent topology and differential geometry on a mathematical point is given in particular with purposes in physics in brain. All easy thoughts are systematically supplied together with sketches of the proofs of so much statements. gentle finite-dimensional manifolds, tensor and external calculus working on them, homotopy, (co)homology concept together with Morse concept of serious issues, in addition to the speculation of fiber bundles and Riemannian geometry, are taken care of. Examples from physics include topological fees, the topology of periodic boundary stipulations for solids, gauge fields, geometric levels in quantum physics and gravitation.

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