%0 Journal Article
%T K-duality for stratified pseudomanifolds
%A Claire Debord
%A Jean-Marie Lescure
%J Mathematics
%D 2008
%I arXiv
%X This paper is devoted to the study of Poincar\'e duality in K-theory for general stratified pseudomanifolds. We review the axiomatic definition of a smooth stratification $\fS$ of a topological space $X$ and we define a groupoid $T^{\fS}X$, called the $\fS$-tangent space. This groupoid is made of different pieces encoding the tangent spaces of the strata, and these pieces are glued into the smooth noncommutative groupoid $T^{\fS}X$ using the familiar procedure introduced by A. Connes for the tangent groupoid of a manifold. The main result is that $C^{*}(T^{\fS}X)$ is Poincar\'e dual to $C(X)$, in other words, the $\fS$-tangent space plays the role in $K$-theory of a tangent space for $X$.
%U http://arxiv.org/abs/0801.3597v4