Questions tagged [frechet-manifold]
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14
questions with no upvoted or accepted answers
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Are these two concepts of a differential form on the loop space equivalent?
Notation:
Let $X$ denote a smooth manifold (without boundary) and define $LX = C^{\infty}(S^1, X)$ to be the loop space on $X$.
In the context of loop space homology and the supersymmetric path ...
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Is the symplectomorphism group of a compact manifold a tame Fréchet Lie subgroup of $\operatorname{Diff}(X)$?
In the famous paper Hamilton, Richard S. The inverse function theorem of Nash and Moser.
Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 1, 65–222, Hamilton introduced the category of tame Fréchet Lie ...
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Is the space of analytic sections of a vector bundle a Fréchet space?
Let $\pi : E \to M$ a smooth vector bundle of finite rank, where both $E$ and $M$ are finite dimensional smooth manifolds, and $M$ is compact. I already know that the space $\Gamma^\infty(M,E)$ of ...
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Regular maps between Fréchet manifolds and pullbacks
An oft-used example of a regular map of finite-dimensional smooth manifolds is a submersion. We have the well-known result that the pullback of a submersion exists and is a submersion. For Fréchet ...
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Global analysis on punctured surfaces
Global analysis on open manifolds seems pretty hard. For one, the space of $C^{n,\alpha}$ functions on an open manifold need not be a tame Fréchet space (see the post Are smooth functions tame? for ...
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Convex subsets of infinite dimensional spaces up homeomorphism
Let $C$ be a convex, infinite-dimensional, non-locally-compact subset of a separable Frechet space.
If $C$ is a closed subset (or more generally, if $C$ is completely metrizable), then it is known ...
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Loop space: various manifold structure.
While reading articles, Sometimes i see collection of all smooth loops as hilbert manifold(pre). Sometime i see this space as banach manifold. Sometime i see this sapce as nuclear frechet space.
Can ...
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Why is the space of smooth sections complete?
This page is about the space of sections:
Let $E \stackrel{\mathrm{fb}}{\rightarrow} \Sigma$ be a smooth vector bundle. On its real vector space $\Gamma_{\Sigma}(E)$ of smooth sections consider the ...
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Banach tori: classification up to Fréchet homeomorphisms
Consider the set $T$ in $l_p$ defined as closure of
\begin{equation}
T = \{ (x_1,\dotsc,x_n,\dotsc): x_j = \frac{1}{2^{(j/p)}} e^{it_j}, t_j \in \mathbb{R}/\mathbb{Z} \}.
\end{equation}
This seems to ...
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When does an analytic submanifold descend to the quotient?
Let $\pi : M \to B$ be a smooth principal bundle with group $G$, where $M$ is an analytic (Fréchet, in my case) manifold, $B$ is a smooth (Fréchet) manifold and $G$ is a smooth (Fréchet) Lie group. ...
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What is the relationship between a metric and the Frechet structure
Let $M$ be a smooth, closed m dimensional manifold. Let $K\subset M$ be a smooth stratifold inside $M$. I'd like to show that $\mathop{Diff}(M,K)$ is a Frechet submanifold of $\mathop{Diff}(M)$. ...
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Is there a version of Hamilton's infinite dimensional family of implicit function theorems which gives us a submersion map?
Hamilton, in his notes on "Inverse Function Theorem of Nash and Moser" states a theorem(1.1.3 on Page 172), where a given nonlinear map between tame Frechet spaces is locally surjective, if ...
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Subspace of smooth Foliations inside smooth Distributions - Is it a Frechet submanifold or atleast a Retraction?
Assume M is a closed manifold. Does the set of smooth foliations on M form a Frechet submanifold inside the Frechet manifold consisting of smooth distributions?
If not, can the set of smooth ...
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Tangent space and a subset of a tame Lie group
I am curious if the set of all orientation-preserving diffeomorphisms with a given rotation number is a tame Lie subgroup or a tame submanifold of all orientation-preserving diffeomorphisms on the ...
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