Manifold subgroups of the homeomorphism group of a compact \(Q\)-manifold (Q1174486)

It is shown that some special subgroups of the homeomorphism group of a compact Hilbert cube manifold are infinite dimensional (not complete) manifolds. For example: if \(X\) is a compact \(PL\) manifold and \(Q\) denotes the Hilbert cube \(I^ \infty\), then the subgroup \(H^{PL}(X\times Q)\) of the homeomorphism group \(H(X\times Q)\) is an \(\ell_ 2^ f\)- manifold, where \(\ell_ 2^ f\) is the linear span of the natural orthonormal basis of the Hilbert space \(\ell_ 2\) and \(H^{PL}(X\times Q)=\{h\times id\mid h\in H(X\times I^ n)\hbox{ for some } n\in\mathbb{N}\hbox{ and }h\hbox{ is }PL\}\).