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On the Poincaré isomorphism in $K$-theory on manifolds with edges
V. E. Nazaikinskiia, A. Yu. Savinb, B. Yu. Sterninb
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.
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English version:
Journal of Mathematical Sciences, 2010, 170:2, 238–250
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UDC:
515.168.5+517.986.32
Citation:
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “On the Poincaré isomorphism in $K$-theory on manifolds with edges”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 34, PFUR, M., 2009, 109–120; Journal of Mathematical Sciences, 170:2 (2010), 238–250
Citation in format AMSBIB
\Bibitem{NazSavSte09}
\by V.~E.~Nazaikinskii, A.~Yu.~Savin, B.~Yu.~Sternin
\paper On the Poincar\'e isomorphism in $K$-theory on manifolds with edges
\inbook Proceedings of the Crimean autumn mathematical school-symposium
\serial CMFD
\yr 2009
\vol 34
\pages 109--120
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd138}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2588089}
\transl
\jour Journal of Mathematical Sciences
\yr 2010
\vol 170
\issue 2
\pages 238--250
\crossref{https://doi.org/10.1007/s10958-010-0082-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77957743067}
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http://mi.mathnet.ru/eng/cmfd138 http://mi.mathnet.ru/eng/cmfd/v34/p109
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