Topology and geometry for physics / Helmut Eschrig.Material type: TextSeries: Lecture notes in physics ; 822.Publication details: Berlin ; Heidelberg ; New York : Springer, ©2011. Description: 1 online resource (xii, 389 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783642147005; 3642147003; 3642146996; 9783642146992Subject(s): Topology | Geometry, Differential | Geometry | Mathematical physics | Physique | Astronomie | Geometry | Geometry, Differential | Mathematical physics | TopologyGenre/Form: Electronic books. Additional physical formats: Print version:: Topology and geometry for physics.DDC classification: 530.15 LOC classification: QC20 | .E83 2011QC20.7.T65 | E73 2011Online resources: Click here to access online
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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.
Includes bibliographical references and index.
Introduction -- Topology -- Manifolds -- Tensor fields -- Integration, homology and cohomology -- Lie groups -- Bundles and connections -- Parallelism, holonomy, homotopy and (co)homology -- Riemannian geometry -- Compendium.
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