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Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. The book uses many of The book uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life.
Keywords: bundles , metrics , curvature , differential geometry , theoretical physics , differential topology , differentiable manifolds , smooth maps , differential forms , vector fields. Forgot password? Don't have an account? All Rights Reserved. OSO version 0.
University Press Scholarship Online. Sign in. Not registered? Sign up. Publications Pages Publications Pages. Users without a subscription are not able to see the full content. Authors Affiliations are at time of print publication. Print Email Share This. Show Summary Details. Subscriber Login Email Address. Password Please enter your Password. Library Card Please enter your library card number. View: no detail some detail full detail. Front Matter Title Pages Preface.
End Matter List of lemmas, propositions, corollaries and theorems List of symbols Index. All rights reserved. Powered by: Safari Books Online.
Every chapter is preceded by a paragraph or two or even more leading the reader gently into the particular part of the forest that lies ahead: a very nice touch. Here are three samples. These introductions tend to go far to give the reader a sense, before the fact, of what the purpose and stresses are of what he is about to encounter. This is clearly a very good pedagogical ploy.
Differential Geometry: Bundles, Connections, Metrics and Curvature
Clifford Henry Taubes. Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Differential Geometry uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life. Helpfully, proofs are offered for almost all assertions throughout. All of the introductory material is presented in full and this is the only such source with the classical examples presented in detail.
Clifford Henry Taubes born February 21,  is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry , and low-dimensional topology. His brother, Gary Taubes , is a science writer. Taubes received his Ph. Soon, he began applying his gauge-theoretic expertise to pure mathematics. His work on the boundary of the moduli space of solutions to the Yang-Mills equations was used by Simon Donaldson in his proof of Donaldson's theorem. In a series of four long papers in the s collected in Taubes , Taubes proved that, on a closed symplectic four-manifold, the gauge-theoretic Seiberg—Witten invariant is equal to an invariant which enumerates certain pseudoholomorphic curves and is now known as Taubes's Gromov invariant.