Some homotopy properties of the homeomorphism groups of 𝑅^{∞} (𝑄^{∞})-manifolds

Liem, Vo Thanh

doi:10.1090/S0002-9939-1987-0883423-X

Some homotopy properties of the homeomorphism groups of $\textbf {R}^ \infty$ $(Q^ \infty )$-manifolds
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Proc. Amer. Math. Soc. 100 (1987), 169-174 Request permission

Abstract:

In this note we will prove that, given an ${R^\infty }({Q^\infty })$-manifold $M$, there is a deformation of $\operatorname {Homo}(M)$ into $\operatorname {Homeo}(M)$ whose final stage is a weak homotopy equivalence, and that if $M$ has the homotopy type of a finite simplicial complex, then $\operatorname {Homeo}(M)$ is an $\operatorname {ANE}(\mathcal {C}\mathcal {W}(\mathcal {M}))$ and an $\operatorname {ANE}(\mathcal {C}\mathcal {W}(\mathcal {C}),{G_\delta })$.

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An

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-manifolds

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