Anonymous
6/2/2025, 10:45:35 PM
No.16684791
>>16684721
You don’t need Frechet and Banach manifolds for vanilla diff geo unless you’re doing calculus of variations or something like geometric quantization.
As per your question on what it can serve as a prerequisite to, the aforementioned things, gauge theory mentioned by (You), symplectic geometry, hardcore Lie theory (with all the root system and Dynkin diagram business), and possibly things like homotopy and cohomology in algebraic topology as many such constructions use diff geo tools.
You don’t need Frechet and Banach manifolds for vanilla diff geo unless you’re doing calculus of variations or something like geometric quantization.
As per your question on what it can serve as a prerequisite to, the aforementioned things, gauge theory mentioned by (You), symplectic geometry, hardcore Lie theory (with all the root system and Dynkin diagram business), and possibly things like homotopy and cohomology in algebraic topology as many such constructions use diff geo tools.