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Results tagged with infinite-dimensional-manifolds
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user 45
8
votes
Fréchet manifolds vs ILH manifolds
It's been a while since I looked at this so take this with the proverbial pinch of salt ...
The key thing (as far as I remember) with ILH manifolds is not the model space but the transition functions …
- 26.8k
6
votes
Are infinite dimensional constructions needed to prove finite dimensional results?
I suspect that the true answer is "No", there isn't a truly finite dimensional result that can't be proved using only finite dimensional means. One reason for thinking that is that (naturally) the fi …
- 26.8k
11
votes
$\infty$-forms and $\infty$-plectic geometry
In the words of Bob the Builder: "Yes, we can."[1]
At the outset, I'll like to note that my thesis was called "A construction of semi-infinite de Rham cohomology".
There's a nice bit to the story an …
- 26.8k
10
votes
Accepted
What is the infinite-dimensional-manifold structure on the space of smooth paths mod thin ho...
Okay, you asked for it!
Question: What is the manifold structure on $P^1(M)$?
Answer: There isn't one.
Update: The biggest failing is actually that the obvious model space is not a vec …
- 26.8k
10
votes
Topology of function spaces?
First off, you want your source space, $X$, to be compact (technically, sequentially compact will do). If you don't have that, $C(X,Y)$ need not be locally contractible so no hope of a manifold struc …
- 26.8k
16
votes
Accepted
Loop Spaces as Generalized Smooth spaces or as Infinite dimensional Manifolds?
They are the same.
If you want the full gory details, read "A Convenient Setting of Global Analysis" by Kriegl and Michor (available as a free PDF via the AMS bookstore). For a gentler approach, rea …
- 26.8k