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.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 34, Proceedings of KROMSH, 2009.
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Nazaikinskii, V.E., Savin, A.Y. & Sternin, B.Y. On the Poincaré isomorphism in K-theory on manifolds with edges. J Math Sci 170, 238–250 (2010). https://doi.org/10.1007/s10958-010-0082-z
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DOI: https://doi.org/10.1007/s10958-010-0082-z