Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ‘Thoroughly recommended’ by The Physics Bulletin, this volume’s physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.
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Preface1. Basic Notions of Topology and the Value of Topological Reasoning2. Differential Geometry: Manifolds and Differential Forms3. The Fundamental Group4. The Homology Groups5. The Higher Homotopy Groups6. Cohomology and De Rhan Cohomology7. Fibre Bundles and Further Differential Geometry8. Morse Theory9. Defects, Textures, and NHomotopy Theory10. Yang-Mills Theories: Instantons and Monopoles Further Reading Subject Index
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