Lecture Notes on Differentiable Manifolds
by Jie Wu
Publisher: National University of Singapore 2004
Number of pages: 78
Contents: Tangent Spaces, Vector Fields in Rn and the Inverse Mapping Theorem; Topological and Differentiable Manifolds, Diffeomorphisms, Immersions, Submersions and Submanifolds; Examples of Manifolds; Fibre Bundles and Vector Bundles; Tangent Bundles and Vector Fields; Riemann Metric and Cotangent Bundles; Tensor Bundles, Tensor Fields and Differential Forms; Orientation and Integration; The Exterior Derivative and the Stokes Theorem.
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by Bjorn Ian Dundas - Johns Hopkins University
This is an elementary text book for the civil engineering students with no prior background in point-set topology. This is a rather terse mathematical text, but provided with an abundant supply of examples and exercises with hints.
by Karl-Hermann Neeb - FAU Erlangen-Nuernberg
From the table of contents: Basic Concepts (The concept of a fiber bundle, Coverings, Morphisms...); Bundles and Cocycles; Cohomology of Lie Algebras; Smooth G-valued Functions; Connections on Principal Bundles; Curvature; Perspectives.
by Ana Cannas da Silva
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The historical driving force of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. This text is occupied with the theory of differential forms and the exterior derivative.