by Neil Lambert
Publisher: King's College London 2011
Number of pages: 59
From the table of contents: Manifolds (Elementary Topology and Definitions); The Tangent Space; Maps Between Manifolds; Vector Fields; Tensors; Differential Forms; Connections, Curvature and Metrics; Riemannian Manifolds.
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In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.
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One of the principal aims of surgery theory is to classify the homotopy types of manifolds using tools from algebra and topology. The algebraic approach is emphasized in this book, and it gives the reader a good overview of the subject.
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