# Questions tagged [infinite-dimensional-manifolds]

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### Couniversality of Lie integration in different categories of manifolds/smooth spaces

A fairly reasonable interpretation of Lie II and Lie III seems to be that the category of Lie algebras is a coreflective subcategory of the category of Lie groups, so that the Lie group integrating a ...
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### Infinite dimensional smooth projective geometry

Are there two infinite dimensional (Banach or Hilbert) manifolds $(P,L)$ which satisfy the axioms of a smooth projective geometry desribed in this page: Smooth Projectove Geometry
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### A smooth map on a Banach manifold whose pointwise rank is finite but its rank is not globally bounded

Is there a connected Banach manifold $M$ and a smooth map $f:M \to M$ such that the rank of $Df_x$ is finite for every $x\in M$ but this rank is not uniformly bounded
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### Finite-dimensional argument for Morse-Smale pairs?

Using the Sard-Smale theorem, it is relatively easy to show that Morse-Smale pairs on a manifold $M$ (i.e. pairs $(f,g)$ where $g$ is a metric on $M$, $f$ is a Morse function on $M$, and the stable/...
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### Smooth derivations of a Banach space

Let $E$ be a real (or complex) Banach space. By $C^\infty(E)$ we mean the space of all functions $f:E\to \mathbb{R}(f:E\to \mathbb{C})$ which are smooth in the sense of Frechet diffetentiability. A ...
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### What is the manifold structure of smooth path on infinite dimensional manifolds?

What is the manifold structure of smooth path on infinite dimensional manifolds? In the the paper "manifolds of smooth maps by Michor", it was mentioned that it is possible to put manifold structure ...
On an exact Hamiltonian system $(M,d\alpha,H)$ define the Rabinowitz action functional $$\mathcal{A}^H \colon C^\infty(\mathbb{S}^1,M) \times (0,+\infty) \to \mathbb{R}$$ by \mathcal{A}^H(\gamma,\...