I am interested in proposition 3.7 in Salvatore's `Configuration spaces with summable labels'. The result states that the bar construction on the Fulton-Macpherson operad is isomorphic to the FM-operad itself. In his proof, the author claims that if you take the manifold with corners $F_n(i)$ and for each face $S$ of $F_n(i)$ of codimension $d$, glue a copy of $S \times [0,1]^d$, then this is diffeomorphic to the original manifold $F_n(i)$. I was wondering whether this is a general result to do with manifolds with corners and if so where can it be found in the literature?
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What do you mean by 'found in the literature'? – Nick Oct 01 '14 at 10:59
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Basically is there a reference for the result if it's true? – Dean Barber Oct 02 '14 at 09:46