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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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closed as not a real question by Ryan Budney, Chris Godsil, Kevin Walker, Theo Buehler, Will Sawin Dec 5 '12 at 21:48

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

    
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? –  Martin Dec 5 '12 at 20:46
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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. –  Ryan Budney Dec 5 '12 at 21:03
    
@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. –  Mozibur Ullah Dec 5 '12 at 22:05
    
@Ryan: I'd agree it isn't focused enough, but I'd dispute its unmotivated. –  Mozibur Ullah Dec 5 '12 at 22:05