Simple question, but I started working with Lean after Lean 4 came out, so I'm not familiar with Lean 3. To what extent have the Mathlib3 differential topology and differential geometry libraries been ported to Mathlib4? What is the next step for developing these theories in Mathlib4?
The answer to any questions of the form "What is the status of mathlib3's [X] in mathlib4" can be answered with the porting dashboard, where you can search for file based on its mathlib3 name.
That will tell you whether it has been ported already: if so, it will tell you where it now resides in mathlib4; and if not, it will tell you how many files remain before it can be ported.
The next step towards porting
geometry/manifolds to Lean 4 is porting the file
cont_mdiff, see https://github.com/leanprover-community/mathlib4/pull/4656
The main obstacle is that Lean 4
simp can't apply lemmas about
Prod s t to
ModelProd s t.