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Where can I find some simple examples of pullbacks and pushforwards between manifolds. Specifically examples that show the details of the computations.

Wintermute
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  • Pullbacks and pushforwards of what: vector fields? differential forms? vector bundles? other? – Santiago Canez Sep 20 '13 at 18:16
  • Of maps between manifolds. – Wintermute Sep 20 '13 at 18:25
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    We push forward/pull back objects defined on manifolds by maps between manifolds. You can pull back/push forward a map by another map but this is just the composition - I'm guessing you're thinking about something else? – Anthony Carapetis Sep 22 '13 at 05:13
  • Given the simplicity of the question's wording, I think it's very likely OP was simply asking about the canonical pushforward of the tangent bundle (of some simple manifold) induced by a map (preferably a simple one) and ditto for the pullback of the cotangent bundle. – Arturo don Juan Jul 12 '18 at 18:04
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    I know its been more than 5 years since this question has been asked but i hope this answer will help others, there are plenty of numerical examples in the book A "Visual Introduction to Differential Forms and Calculus on Manifolds (2019, Springer International Publishing)" by Fortney, J.P. – Josyula Krishna Aug 06 '19 at 08:43

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Take a look at An Introduction to Differential Geometry through Computation by Mark Fels.

Peter4075
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