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Results tagged with jets
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user 56938
4
votes
1
answer
239
views
Semi-holonomic jets in synthetic differential geometry
Unfortunately, he doesn't seem to cover semi-holonomic jets in his text, and I find the usual definition of semi-holonomic jets to be difficult to interpret geometrically. … The path dependence for semi-holonomic jets should be less strict in some sense. …
- 6,025
2
votes
2
answers
333
views
Constructing jet bundles from a cocycle of smooth transition functions
Suppose we are given an open cover $\mathcal{U}=(U_{i})_{i \in I}$ of a smooth manifold $M$, a cocycle of smooth transition functions $g_{ij}: U_{ij} \to G$ where $G$ is a Lie group, and a (not necess …
- 6,025
7
votes
1
answer
627
views
Jets in synthetic differential geometry
As I understand it from Kostecki's notes, the $k$-jet $j^k f$ of a function $f: R^n \to R^m$ should be the map $$f^{D_k(n)} : {(R^n)}^{D_k(n)} \to (R^m)^{D_k(n)},$$
where $$D_k(n) = \{(x_1, \ldots, x_ …
- 6,025