V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “On the Poincaré isomorphism in <nobr>$K$</nobr>-theory on manifolds with edges”, CMFD, 2009, Volume 34,Pages <nobr>109

On the Poincaré isomorphism in $K$-theory on manifolds with edges

V. E. Nazaikinskii^a, A. Yu. Savin^b, B. Yu. Sternin^b

^a A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
^b Independent University of Moscow

Abstract: In this paper, the Poincaré isomorphism in $K$-theory on manifolds with edges is constructed. It is shown that the Poincaré isomorphism can be naturally constructed in terms of noncommutative geometry. More precisely, we obtain a correspondence between a manifold with edges and a noncommutative algebra and establish an isomorphism between the $K$-group of this algebra and the $K$-homology group of the manifold with edges, which is considered as a compact topological space.

UDC: 515.168.5+517.986.32