$\DeclareMathOperator\PL{PL}$Consider the group $\PL\_{n,n-1}$ of orientation preserving PL self-homeomorphisms of $\mathbb R^n$ that also preserve $\mathbb R^{n-1}$ pointwise. It is usually understood as a simplicial group whose $k$-simplices are PL self-homeomorphisms $\mathbb R^n\times\Delta^k\to \mathbb R^n\times \Delta^k$ commuting with the projection on $\Delta^k$. Is this simplicial group contractible?



Is $\operatorname{PL}_{n,n-1}$ contractible?
The answer is yes, see the discussion above with [Connor Malin](https://mathoverflow.net/users/134512/connor-malin).


