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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 are generalisations of Banach Manifolds, so they too have the same property.

Michor & Krigel, say 'this does not make them [Banach Manifolds] interesting [enough]' in The convenient setting of Global Analysis,

What are the other directions to take, when looking for interesting infinite-dimensional manifolds, (besides the one Michor/Kriegel outline in their book). And has a canonical choice begun to establish itself yet?

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  • $\begingroup$ I don't understand what this question is about: What would you consider to be interesting and what would be a canonical choice for what end? Possibilities for what? Moreover, Henderson's result says that if a Fréchet manifold is separable and metrizable then it embeds as an open subset into $\ell_2$. Finally, what exactly is the difference between the present question and your earlier question mathoverflow.net/questions/90656? $\endgroup$
    – Martin
    Commented Dec 5, 2012 at 20:46
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    $\begingroup$ Your question appears to me to be along the lines of "tell me something about infinite dimensional manifolds", in that it's rather undirected and unmotivated. $\endgroup$
    – Ryan Budney
    Commented Dec 5, 2012 at 21:03
  • $\begingroup$ @user49437: my first question was reacting against Michors assertion that Banach Manifolds aren't interesting. Obviously they're not flexible enough notion for the purposes he wants to put them to. $\endgroup$
    – Mozibur Ullah
    Commented Dec 5, 2012 at 22:05
  • $\begingroup$ @Ryan: I'd agree it isn't focused enough, but I'd dispute its unmotivated. $\endgroup$
    – Mozibur Ullah
    Commented Dec 5, 2012 at 22:05
  • $\begingroup$ @Martin: It's what Michor et al was saying about Banach manifolds that made them uninteresting. Not me. I didn't know enough then to form a judgement. It's seems pretty silly to me to knock back a question which is asking about more informed judgement. $\endgroup$
    – Mozibur Ullah
    Commented Oct 31, 2021 at 15:56

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