I originally posted this question on StackExchange, where it was suggested I post here. It was also suggested I read about Hilbert manifolds and Fréchet manifolds. Nevertheless, I …

On the first page of Chapter 1 of Rieffel's Deformation Quantization for Actions of $ \mathbb{R}^{d} $, Rieffel defines a family of seminorms on the space $ A^{\infty} $ of smooth …

This question stems from Jeff Rubin's earlier MO question and a follow-up that I posted. The former recalls the following result proved by both Serge Lang (Fundamentals of Differ …

According to wikipedia, by a theorem of Henderson '69, infinite-dimensional Frechet Manifolds embed as open subspaces of Hilbert Space. They need to be seperable & metric. They …

How to calculate the DeRham cohomology of the free loop space $LM= C^\infty(S^1,M)$ as a Frechet manifold?. Edit: It will be enough for me to know: When $H^1_{DR}(LM)$ is no …

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 …

Given two smooth manifolds $M$ and $N$, it is known that if $M$ is compact, then $C^\infty(M,N)$ is a Fréchet manifold whose tangent space at $f \in C^\infty(M,N)$ is the space $$T …

Let $M$ be a manifold equipped with a pair of surjective submersions $N_1 \stackrel{p_1}{\leftarrow} M \stackrel{p_2}{\rightarrow} N_2$ where $dim N_1 = dim N_2 = n$. Then we can f …

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 …

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 …

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 submers …

hi, does anyone know a good book or some lecture notes on the theory of 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 …

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 …

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 fun …