In this MO question on the classification of sphere bundles there is an answer claiming that the group of PL-homoemorphisms of the sphere $\operatorname{PLHomeo}(S^n)$ is homotopic to $\operatorname{O}(n+1)$. Can someone give me a reference of this fact?
Also, do you have any book recommendation for the homotopy type of $\operatorname{Homeo}(S^n)$, $\operatorname{PLHomeo}(S^n)$ and $\operatorname{Diff}(S^n)$?
