K–duality for stratified pseudomanifolds

This paper continues our project started in [11] where Poincaré duality in K -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 S of a topological space X and we define a groupoid T S X , called the S-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 T S X using the familiar procedure introduced by Connes for the tangent groupoid of a manifold.The main result is that C .T S X / is Poincaré dual to C.X /, in other words, the S-tangent space plays the role in K -theory of a tangent space for X .