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Let $M$ be a manifold. If $M$ is smooth, it is clear what $\text{Diff}(M)$ should be, namely it should be the set of diffeomorphisms of $M$ equipped with the topology in which a sequence of diffeomorphisms converges if they and all their derivatives converge. If $M$ is PL, I have seen many assertions that it is not reasonable to regard the set $PL(M)$ of PL homeomorphisms of $M$ as a space, but instead one should replace it by a simplicial group. Why is that? What pathologies are we trying to avoid?

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