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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Classifying spaces for foliations with isolated singularities

Author: Peter Greenberg
Journal: Trans. Amer. Math. Soc. 304 (1987), 417-429
MSC: Primary 57R32; Secondary 58H10
MathSciNet review: 906823
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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{\vert _{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}}$.

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Article copyright: © Copyright 1987 American Mathematical Society