can one consider Taylor expansions of functions defined between smooth manifolds? If so, is there a reference for learning more about it? Thanks
Asked
Active
Viewed 175 times
1
-
differential geometry – Ittay Weiss Nov 22 '13 at 21:22
-
you answer is too general.. – PtF Nov 22 '13 at 21:25
-
It precisely answers your question though. – Ittay Weiss Nov 22 '13 at 21:28
-
ok, could you be a bit more specific? – PtF Nov 22 '13 at 21:35
1 Answers
2
Indeed you can.
If you have $\operatorname{f} : M^m \to N^n$ then locally this is just a map $\mathbb{R}^m \to \mathbb{R}^n$.
If $\operatorname{f}(x)=y$ then we phrase the local situation in terms of "germs" $\operatorname{f} : (M,x) \to (N,y)$ and "jets".
One famous reference is "Stable mappings and their singularities" by Golubitsky & Guillemin.
Fly by Night
- 32,272