I'm looking for a good source for a large collection of Differential Manifolds/Geometry questions covering a subset of the following topics:

inverse function theorem, local coordinates, induced structures, tangent bundle, regular values, transversality, classical Lie groups, tubular neighborhoods, vector fields and flows, differential forms and de Rham cohomology, integration of forms and Stokes Theorem, relationship to singular homology, de Rham theorem, Riemannian metrics.

Multiple sources are welcome. I do have access to A Comprehensive Introduction to Differential Geometry by Spivak and Topology and Geometry by Bredon. Does anyone else know where I can find more questions? I am particularly interested in concrete problems concerning specific manifolds.

In fact, if there is a text available that teaches geometry by deeply dissecting a large collection of examples I would be very appreciative.

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    $\begingroup$ Lee's Smooth Manifolds is pretty easy to read, so far so good, I'm in Chapter 3 with a student this semester. I also like Tu's manifold text and Conlon is worthwhile. There are so many nice manifold texts these days. $\endgroup$ – James S. Cook Jan 26 '14 at 2:58

Sounds like you are looking for this:

Algebra and Analysis on Differentiable Manifolds: A Workbook for Students and Teachers.

Its chapters deal with, in that order: Differentiable Manifolds, Tensor Fields and Differential Forms, Integration on Manifolds, Lie Groups, Fibre Bundles and Riemannian Geometry.

All problems have very detailed solutions and many tackle specific manifolds, so you won't be left hanging on abstractions.

  • $\begingroup$ This book, my friend, seems fantastic! Thank you very much. $\endgroup$ – breeden Dec 2 '14 at 20:03

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