Manifolds 18 | Regular Value Theorem (abstract version)

[@洛叶-b1y]

definitely thanks a lot from a math junior currently having geo topology! your demonstration is very clear

[@shreyammishra2203]

This video was absolutely delightful to watch! Keep these coming; can't thank you enough for making these for free :)

[@ko-prometheus]

I want to apply this knowledge to MetaPhysics.

[@arghyaprati2497]

very nice illustrations of concepts

[@brightsideofmaths]

Thank you very much! An thanks for your support!

[@tensorfeld295]

Thank you! :D

[@tim-701cca]

great series and nice drawings and writing!! It makes us easy to read and follow. Are they draw and written by hand?

[@brightsideofmaths]

Thank you! Most of my videos is my handwriting. See also tbsom.de/s/up

[@franzmaina3080]

Hi, why isn't the 19th episode available? Keep up the good work!!

[@brightsideofmaths]

Thanks. Episode 19 is in early access for supporters :)

[@StratosFair]

Thank you for this crystal clear explanation of the more general version of this theorem, very helpful ! Just a question : how do we know that the Jacobian matrix (or its rank) is independent of the choice of charts h and k ?

[@brightsideofmaths]

Very good question! The answer is, as always, in the transition maps. You can change charts with diffeomorphisms which don't change the rank.

[@StratosFair]

@@brightsideofmaths oh right, the diffeomorphisms are invertible so the rank doesn't change when we compose with them !

[@SlipperyTeeth]

14:28 The exceptions you list would not be in the GL.

[@brightsideofmaths]

The Jacobian matrix is not square anyway ;)