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edited Feb 12 at 7:06

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Group Does the group of compactly supported diffeomorphisms not havinghave the homotopy type of a CW complex?

dg.differential-geometry at.algebraic-topology gt.geometric-topology differential-topology

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asked Feb 9 at 16:52

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Group of compactly supported diffeomorphisms not having the homotopy type of a CW complex

It is known that the group of diffeomorphisms of a compact manifold with the natural $C^{\infty}$ topology has the homotopy type of a countable CW complex. See for instance this thread: Is the space of diffeomorphisms homotopy equivalent to a CW-complex?

The group $Diff_c(M)$ of compactly supported diffeomorphisms is a nuclear LF space: http://www.mat.univie.ac.at/~michor/manifolds_of_differentiable_mappings.pdf With this topology does it have the homotopy type of a CW complex?

dg.differential-geometry at.algebraic-topology differential-topology