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Results tagged with infinite-dimensional-manifolds
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user 17047
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Symplectic Reduction on infinite dimensional manifolds
Yes, the form $\Omega$ is closed and defines indeed a weak symplectic structure. This can be verified by a direct but a bit messy calculation. A cleaner way would be to generalize the ideas of Vizman: …
- 5,824
1
vote
On the orbit of a Fréchet Lie group action
I'm not aware of a precise characterization of when the orbits are initial submanifolds in infinite dimensions. In fact, the manifold structure on the orbits is a hard problem even for $G$-actions on …
- 5,824
2
votes
Frechet Lie groups and their subgroups
Concerning your second point, it is no longer true that closed subgroups are Lie subgroups (even in the Hilbert setting). The corresponding result in infinite dimensions needs additional assumptions c …
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2
votes
the tangent space $T_J\mathcal J^k$ of the space of $\omega$-compatible almost complex struc...
An almost complex structure gives you a reduction of the frame bundle $LM$ from $Sp(2n)$ to $U(n)$. Hence the space $\mathcal{J}$ of all almost complex structures compatible with the symplectic form i …
- 5,824
7
votes
Accepted
Submersion theorem for smooth tame Frechet manifolds
There are a few works which study submersions in the locally convex setting. The most extensive (and recent) is by Helge Glöckner (http://arxiv.org/abs/1502.05795). Note that the basic results about s …
- 5,824
8
votes
Accepted
Smooth structure on the space of sections of a fiber bundle and gauge group
Your intuition is right. To endow the space of sections of a fiber bundle $F$ with a manifold structure at $\phi \in \Gamma^\infty(F)$ you consider a tubular neighborhood (respecting the fiber structu …
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