# Differential Geometry, Lie Groups, and Symmetric Spaces

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Language: English

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From the table of contents: Topology (Homotopy, Manifolds, Surfaces, Homology, Intersection numbers and the mapping class group); Differentiable manifolds; Riemannian geometry; Vector bundles; Lie algebras and representations; Complex manifolds. Dimension has gone through stages of being any natural number n, possibly infinite with the introduction of Hilbert space, and any positive real number in fractal geometry. Within this interpretation, Euclid’s fifth postulate was an empirical finding; non-Euclidean geometries did not apply to the real world.

Pages: 641

Publisher: American Mathematical Society (June 12, 2001)

ISBN: 0821828487

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Introduction to Geometry of Manifolds with Symmetry (Mathematics and Its Applications)

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Exploring Curvature

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