Manifolds and Differential Forms
by Reyer Sjamaar
Publisher: Cornell University 2017
Number of pages: 171
The course covers manifolds and differential forms for an audience of undergraduates who have taken a typical calculus sequence at a North American university, including basic linear algebra and multivariable calculus up to the integral theorems of Green, Gauss and Stokes.
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by Neil Lambert - King's College London
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.
by Andreas Kriegl, Peter W. Michor - American Mathematical Society
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory.
by Andrew Ranicki - Cambridge University Press
Noncommutative localization is a technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. The applications to topology are via the noncommutative localizations of the fundamental group rings.
by C. Nash - arXiv
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.