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Introduction to Differentiable Manifolds

POSTED BY: Brian Beckman
3 Replies

Hello Brian,

This is absolutely what I have been waiting for years! I have been educated in differential Topology in the... Bourbaki style. You do explain the other way round. I guess anyone here can understand this brilliant lesson.

As to the WL it lacks the even elementary functions to do ... elementary differential Geometry, or we have to type hundreds of lines of code to get something very interresting. (I have been using it since 1991, version 1.1.a)

Thank you very much.

Jean-Michel Paris Retired mathematician

Dear Jean-Michel,

Thank you for the kind words! I am delighted that I hit a sweet spot even in the mind of a hard-boiled mathematician!

I recently discovered the xAct library (my Reference [22]). It looks very promising for checking hand calculations on manifolds. I am currently evaluating it in some detail in my related work. My current challenge is to navigate a large variety of adjoint representations necessary for force models in geometric integrators (hinted at in my paper).

I'll have more notebooks along these lines in the coming months.


POSTED BY: Brian Beckman

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