Triangulations of manifolds and combinatorial bundle theory: an announcement

For a given compact $\mathrm{PL}$-manifold $X$, studied is the category $\mathbf{CM}(X)$ of combinatorial-manifold structures on $X$, whose objects of $\mathbf{CM}(X)$ are abstract simplicial complexes $S$ with geometric realization $\mathrm{PL}$-homeomorphic to $X$, and while the morphisms are “combinatorial subdivisions.” The geometric realization $B\mathbf{CM}(X)$ of the nerve of $\mathbf{CM}(X)$ is announced to be homotopy equivalent to the classifying space $B\mathrm{PL}(X)$ of the simplicial group $\mathrm{PL}(X)$: $B\mathbf{CM}(X)\approx B\mathrm{PL}(X)$.