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This book is an elementary introduction to the geometrical methods and notions used in special and general relativity. Particular emphasis is placed on the ideas concerned with the structure of spacetime and those which play a role in the Penrose–Hawking singularity theorems.
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This mathematically rigorous survey of the special theory of relativity also details the physical significance of that mathematics. In addition to kinematics, particle dynamics and electromagnetic fields it treats subjects usually bypassed at elementary level.
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A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds.