Classifying spaces for foliations with isolated singularities
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- by Peter Greenberg PDF
- Trans. Amer. Math. Soc. 304 (1987), 417-429 Request permission
Abstract:
Let ${\Gamma ^a} \subset \Gamma$ be transitive pseudogroups on ${{\mathbf {R}}^n}$, 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 ${\mathbf {R}}$ is weakly homotopy equivalent to $B{\mathbf {R}}{\ast }B{\mathbf {R}}$.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 304 (1987), 417-429
- MSC: Primary 57R32; Secondary 58H10
- DOI: https://doi.org/10.1090/S0002-9947-1987-0906823-2
- MathSciNet review: 906823