2017
DOI: 10.1007/s11005-017-1011-6
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Orbispaces as differentiable stratified spaces

Abstract: We present some features of the smooth structure and of the canonical stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invariance of these structures—it allows us to talk about the canonical structure of differentiable stratified space on the orbispace (an object analogous to a separated stack in algebraic geometry) presented by the proper Lie groupoid. The canonical smooth structure on an orbispace is studied mainly via Spallek’s framework of differentiabl… Show more

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Cited by 21 publications
(40 citation statements)
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References 51 publications
(123 reference statements)
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“…2.25 are surjective submersions with the following condition: these maps are transversal to the orbits of the Lie groupoids (G and H respectively) and meet every orbit. This fact can be found in [17] and [8], and follows also from proposition A.5.…”
Section: A Second Look At Hausdorff Morita Equivalence Of Singular Fosupporting
confidence: 70%
“…2.25 are surjective submersions with the following condition: these maps are transversal to the orbits of the Lie groupoids (G and H respectively) and meet every orbit. This fact can be found in [17] and [8], and follows also from proposition A.5.…”
Section: A Second Look At Hausdorff Morita Equivalence Of Singular Fosupporting
confidence: 70%
“…inherits from X × R N a structure of a C ∞ -manifold. A good reference for this is the nice extended survey of Crainic and Mestre, [9], that clarifies and explains very interesting results on Lie groupid theory that were confusing in the litterature, in particular they explain the role of the linearization theorem for proper Lie groupoids (theorem 2 in ref.cit.) on the local structure of such groupoids and on their orbit spaces.…”
Section: The Orbit Space O X As a Manifold With Cornersmentioning
confidence: 89%
“…We construct a continuous version of the space described in Example 4.14. Following [10], starting with the principal Z/2-bundle given by the double cover S 1 → S 1 /(Z/2), we construct a transitive groupoid G with G 0 = S 1 /(Z/2) and G 1 = (S 1 × S 1 )/(Z/2), the orbit space of the diagonal Z/2-action on…”
Section: Bredon Homology and Cohomologymentioning
confidence: 99%