Abstract
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 .
Citation
Claire Debord. Jean-Marie Lescure. "$K$–duality for stratified pseudomanifolds." Geom. Topol. 13 (1) 49 - 86, 2009. https://doi.org/10.2140/gt.2009.13.49
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