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Classifying spaces for foliations with isolated singularities. (English) Zbl 0626.58030
Let \(\Gamma^ a\subset \Gamma\) be transitive pseudogroups on \({\mathbb{R}}^ n\), such that, for any element \(g: U\to V\) of \(\Gamma\), there is a locally finite subset \(S\subset U\), such that \(g|_{U-S}\) is an element of \(\Gamma^ a\). We construct \(B\Gamma\), up to weak homotopy type, from \(B\Gamma^ a\) and the classifying spaces of certain groups of germs. As an application, the classifying space of the pseudogroup of orientation-preserving, piecewise linear homeomorphisms between open subsets of \({\mathbb{R}}\) is weakly homotopy equivalent to B\({\mathbb{R}}*B{\mathbb{R}}\).

MSC:
58H05 Pseudogroups and differentiable groupoids
55P99 Homotopy theory
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