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Results tagged with infinite-dimensional-manifolds
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user 46510
3
votes
Accepted
Relation between locally convex calculus and Kriegl & Michor's "convenient setting"
It is actually well known that every smooth map in the Michal-Bastiani (MB) sense (what you call "differential calculus on locally convex spaces") is also smooth in the convenient sense.
For a quick …
- 2,388
3
votes
Manifolds of maps
To go a bit more into the details (elaborating on Thomas comment above):
The result on the differentiability order is classical (going back to Ebin's work in the 60s, culminating in the seminal paper …
- 2,388
2
votes
Accepted
$c^\infty$ topology on $L(E, F)$
Since this was a bit long for a comment, I am posting it here as an answer (though it unfortunately does not answer your question per se).
It is not clear to me in general how the topologies are rela …
- 2,388
18
votes
Accepted
Is the subgroup $\mathrm{Diff}(M,S)$ of $\mathrm{Diff}(M)$ a Lie subgroup?
Before I come to the core of your question concerning the subgroup $\mathrm{Diff}(M,S)$ let us first clarify the terms Lie group and subgroup:
In general there are many different concepts, especially …
- 2,388
2
votes
Accepted
Reconciling some result about the exponential map, the Chow-Rashevskii theorem, and $\mathrm...
This was a bit long for a comment, thus I post it as an answer.
First of all, you have to be very careful with what you actually mean by the exponential here. The flow map to time 1 does NOT exist in …
- 2,388
9
votes
Group of diffeomorphisms and its tangent space i.e. its Lie algebra
For compact manifolds the identification is a consequence of the exponential law for smooth functions. It states that
$$f\colon L\rightarrow C^\infty (K,N)$$
is smooth ($K$ a compact smooth manifold) …
- 2,388