Geodesic
On the Poincar\'e isomorphism in $K$-theory on manifolds with edges
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 34 (2009), pp. 109-120

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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. 
@article{CMFD_2009_34_a4,
     author = {V. E. Nazaikinskii and A. Yu. Savin and B. Yu. Sternin},
     title = {On the {Poincar\'e} isomorphism in $K$-theory on manifolds with edges},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {109--120},
     publisher = {mathdoc},
     volume = {34},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2009_34_a4/}
}
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V. E. Nazaikinskii; A. Yu. Savin; B. Yu. Sternin. On the Poincar\'e isomorphism in $K$-theory on manifolds with edges. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 34 (2009), pp. 109-120. http://geodesic.mathdoc.fr/item/CMFD_2009_34_a4/