All Questions
Tagged with jets smooth-manifolds
7 questions
2
votes
0
answers
55
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How is the $k$-times iterative frame bundle $FF\cdots FM$ associated to the higher order frame bundle $F^k M$?
$\DeclareMathOperator\Gl{Gl}$As I understand it a natural bundle is one for which a diffeomorphism on the base space lifts to an automorphism on the total space of the bundle. It is my understanding ...
- 250
3
votes
0
answers
58
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Jet at a singular point or a submanifold
Let $M$ be a smooth manifold, $p\in M$ and $f\in C^\infty(M\setminus\{p\})$.
We will say that $f$ has a power-law singularity at $p$ of order $\eta$ if for every smooth immersion $\gamma:(-1,1)\to M$ ...
- 1,488
5
votes
2
answers
277
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Equivalence of two definitions of jets of smooth functions
In the literature I have encountered two different definitions of jets of smooth functions, and I was wondering how one could identify these definitions.
One definition is the often encountered ...
- 73
7
votes
1
answer
4k
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Short and elegant definition of the $C^1$ topology
A friend told me that the $\mathbf{C^1}$-topology on the set $C^\infty(M,N)$ of smooth functions between two smooth manifolds $M$ and $N$ can be defined as the coarsest topology making the map
$$
C^\...
- 71
5
votes
0
answers
281
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How to visualize the dual objects of jets of functions?
I work with a smooth $f: M \to \Bbb C$ and I would like to have an object mimicking the concept of "$k$-th order differential" from multivariate calculus. For various reasons that are not important ...
- 5,407
3
votes
1
answer
582
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Jet spaces between non Hausdorff manifolds
I found it very hard to find literature about smooth manifolds that are not required to be Hausdorff. In particular I'm interested in their local properties:
1.) Are the $r$-th order jet bundles $J^r(...
- 137
5
votes
2
answers
1k
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On the smooth structure of the spaces of $k$-jets
I was asking myself, if the following list of conditions is sufficient to determine the usual smooth structure on the spaces of $k$-jets.
the map $j^k f:M\ni x\to j_x^k f\in J^k(M,N)$ is smooth, for ...
- 4,306