State University of Sao Paulo, Sao Paulo, Brazil, 1996. – 699 p. – ISBN-10: 9810222327This work stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and others subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation. It consists of a main text and a topical section. The main text introduces the mathematical ideas and serves as a guide to the topical section.Manifolds General Topology Manifolds Homology Homotopy Manifolds & Charts Differentiable Manifolds Differentiable Structure Tangent Structure Differential Forms Symmetries Fiber Bundles Final Touch Noncommutative Geometry Mathematical Topics The Basic Algebraic Structures Discrete Groups. Braids and Knots Topological Linear Spaces Banach Algebras Representations Variations & Functionals Functional Forms Singular Points Euclidean Spaces and Subspaces Non-Euclidean Geometries Geodesics Physical Topics Hamiltonian Mechanics More Mechanics Statistics and Elasticity Propagation of Discontinuities Geometrical Optics Classical Relativistic Fields Gauge Fields General Relativity De Sitter Spaces Symmetries on Phase Space Glossary and Bibliography
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