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$K$–duality for
stratified pseudomanifolds
Claire Debord and Jean-Marie Lescure |
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Geometry & Topology 13 (2009) 49–86
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Abstract |
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This paper continues our project started in [J. Funct. Anal. 219, 109–133] where Poincaré duality in –theory was studied for singular manifolds with isolated conical singularities. Here, we extend the study and the results to general stratified pseudomanifolds. We review the axiomatic definition of a smooth stratification of a topological space and we define a groupoid , called the –tangent space. This groupoid is made of different pieces encoding the tangent spaces of strata, and these pieces are glued into the smooth noncommutative groupoid using the familiar procedure introduced by Connes for the tangent groupoid of a manifold. The main result is that is Poincaré dual to , in other words, the –tangent space plays the role in –theory of a tangent space for . |
Keywords
singular manifolds, smooth groupoids, Kasparov bivariant
$K$–theory, Poincaré duality
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Mathematical Subject Classification 2000
Primary: 58B34, 46L80, 19K35, 58H05, 57N80
Secondary: 19K33, 19K56, 58A35, 57P99
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References |
Publication
Received: 20 February 2008
Revised: 18 August 2008
Accepted: 4 July 2008
Preview posted: 22 October 2008
Published: 1 January 2009
Proposed: Steve Ferry
Seconded: Ralph Cohen, Wolfgang Lueck
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Authors |
| Claire Debord | |
| Laboratoire de Mathématiques Université Blaise Pascal Complexe universitaire dse Cézeaux 24 Av. des Landais 63177 Aubière cedex France |
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| http://math.univ-bpclermont.fr/~debord/ | |
| Jean-Marie Lescure | |
| Laboratoire de Mathématiques Université Blaise Pascal Complexe universitaire dse Cézeaux 24 Av. des Landais 63177 Aubière cedex France |
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| http://math.univ-bpclermont.fr/~lescure/ | |
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