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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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##### References:
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