# Questions tagged [frechet-manifold]

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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 $\mathop{Diff}(M)$. ...
0answers
106 views

### 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 ...
0answers
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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 ...
3answers
391 views

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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 ...
0answers
300 views

### Regular maps between Frechet 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 Frechet ...
3answers
707 views

### Internal equivalence implies weak equivalence for Frechet Lie groupoids?

It is a known theorem that an internal equivalence of Lie groupoids (finite dimensional manifolds!) - that is an equivalence in the 2-category of Lie groupoids, smooth functors and transformations - ...
3answers
1k views

### Induced map on path manifolds: is it a submersion?

Consider the following claim: Let $p:M \to N$ be a (surjective) submersion of finite-dimensional smooth manifolds. Let $J$ denote one of $[0,1],\ [0,1),\ (0,1]$. Then $p_*:M^J \to N^J$ is a ...
1answer
382 views

### Ind-Frechet manifolds?

Short version: has anyone done geometry on something that is the formal filtered colimit of Frechet manifolds? Longer version: A colleague and I came up with a concept today that seems like we ...
2answers
726 views

### frechet manifolds book

hi, does anyone know a good book or some lecture notes on the theory of frechet manifolds ?
1answer
224 views

### Complement of a closed star-shaped subset in a Frechet space

Let $U$ be the complement of a closed star-shaped subset in a separable infinite-dimensional Frechet space. Since every separable Frechet space is homeomorphic to $l_2$, one knows that $U$ is a ...
3answers
572 views

### Two notions of tangent vector for a Fréchet manifold

Let $X$ be a Frechet or Banach manifold. We can define tangent vectors by equivalence classes of smooth curves. But, we could also define them as derivations of germs of smooth functions. Do these two ...