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Results tagged with infinite-dimensional-manifolds
Search options questions only
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user 4177
11
votes
1
answer
546
views
How manifold-like is Aut(C^n) in the holomorphic category?
This question is similar to, but not the same as this one. Take the space of automorphisms of $\mathbb{C}^n$ in the holomorphic category, with the compact-open topology. For $n=1$ this is just $\mathb …
- 35.5k
8
votes
1
answer
227
views
Is the Borel lemma projection a smooth principal bundle?
Consider the Fréchet spaces $C^\infty(\mathbb{R},\mathbb{R})$ and $\mathbb{R}^\infty$, and the continuous linear map
$$
J\colon C^\infty(\mathbb{R},\mathbb{R}) \to \mathbb{R}^\infty
$$
returning the i …
- 35.5k
11
votes
1
answer
528
views
How many Fréchet manifolds are there?
Clearly the title needs clarifying. Allow me to let "how many" to mean a set larger than a skeleton of the category of Fréchet manifolds and smooth maps, if this category is indeed essentially small.
…
- 35.5k
8
votes
0
answers
227
views
Holomorphic contractibility of GL(H)?
Kuiper's theorem is well-known to give the triviality of the homotopy groups of ${\rm GL}(\mathcal{H})$ for $\mathcal{H}$ a (separable) infinite-dimensional complex Hilbert space. Work of Palais later …
- 35.5k