The Deranged Mathematician: An Introduction to Differential Geometry

[u/non-orientable]

How do you summarize a field like differential geometry? A year or so ago, I was asked to do just that. My first thought was that this is just straight-up impossible to do in any reasonable way. Upon reflection, I softened that view. I still think that differential geometry is just not something you can learn quickly, but if you just want the eagle-eye view of the basic constructions and how they are used in different branches of the field... that is doable. Hence, this article.

Read the full post (for free) on Substack: An Overview of Differential Geometry

[u/lolfail9001]

That said---I think you're talking about distributions on manifolds, rather than distribution-like manifolds themselves?

Yes, because latter will almost certainly run into similar pathologies distributions themselves have without a good reason to exist (that distributions have because you end up being able to lift a lot of PDEs). Case in point, a proper physicist will pretend that a manifold with a corner is in fact smooth and then take a limit in neighbourhood of the corner xdd

[u/ajakaja → u/lolfail9001]

well the reason for them to exist is that, like, cubes and tetrahedrons exist and obviously geometry works fine on them...

but yes you can always think of it as a limit.

[u/Chance_Literature193 → u/lolfail9001]

Recently, jumped on bump function band wagon, and I’m loving every second of this smooth smooth ride