K-duality for stratified pseudomanifolds

摘要

This paper continues our project started in [12] where Poincare 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 Poincare dual to C(X), in other words, the S-tangent space plays the role in K-theory of a tangent space for X.