Orbifold structure gives a natural stratification by open manifolds on its underlying space, where one stratum corresponds to a set of singular points of the same type.
2.
Laurent Siebenmann in his thesis found an invariant similar to Wall's that gives an obstruction to an open manifold being the interior of a compact manifold with boundary.
3.
By construction, it contains X _ { \ mu > \ epsilon } as a dense open submanifold; essentially, it compactifies this open manifold with the symplectic quotient
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