On the Poincaré isomorphism in K-theory on manifolds with edges
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.
KeywordsManifold Vector Bundle Dirac Operator Elliptic Operator Toeplitz Operator
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- 1.M. F. Atiyah, “Global theory of elliptic operators,” in: Proc. Int. Symp. Funct. Anal., Univ. of Tokyo Press, Tokyo (1969), pp. 21–30.Google Scholar
- 2.M. F. Atiyah and R. Bott, “The index problem for manifolds with boundary,” in: Bombay Colloq. Differ. Anal., Oxford Univ. Press, Oxford (1964), pp. 175–186.Google Scholar
- 5.P. Baum and R. G. Douglas, “K-homology and index theory,” in: Operator Algebras Appl., Proc. Symp. Pure Math., 38, Part 1, (1982), pp. 117–173.Google Scholar
- 11.J. Kaminker, “Pseudo-differential operators and differentiable structures,” in: Operator Algebras and K-Theory, Amer. Math. Soc., Providence, Rhode Island (1982), pp. 99–128.Google Scholar
- 12.G. G Kasparov, “Operator K-theory and applications,” in: Itogi Nauki Tekhn. Ser. Sovr. Probl. Mat. Noveishie Resul’taty, 27, VINITI, Moscow (1985), pp. 3–21.Google Scholar