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Hochschild- and Cyclic-Homology of LCNT-Spaces

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Abstract

We define a class of topological spaces ( LCNT spaces ) which come together with a nuclear Fréchet algebra. Like the algebra of smooth functions on a manifold, this algebra carries the differential structure of the object. We compute the Hochschild homology of this algebra and show that it is isomorphic to the space of differential forms. This is a generalization of a result obtained by Alain Connes in the framework of smooth manifolds.

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References

  1. Borel, A.: Intersection cohomology. (Notes of a Seminar on Intersection Homology at the University of Bern, Switzerland, Spring 1983). (English) Progress in Mathematics, Vol. 50, Swiss Seminars. Boston-Basel-Stuttgart: Birkhäuser, 1984

  2. Brasselet, J-P., Pflaum, M.: On the homology of algebras of Whitney functions over sub-analytic sets. Institut de Mathématiques de Luminy, Preprint 2002-02, 2002

  3. Bredon, G.: Topology and Geometry. Graduate Texts in Math 139, Berlin-Heidelberg-New York: Springer, 1991

  4. Brodzki,J., Lykova,Z.: Excision in Cyclic Type Homology of Fréchet Algebras. Bull. Lond. Math. Soc. 33(3), 283–291 (2001)

    MATH  Google Scholar 

  5. Connes, A.: Non-commutative Differential Geometry. Publications Mathematiques IHES 62, 1985

  6. Ewald, C.: Hochschild homology and de Rham cohomology of stratifolds. Dissertation Universität Heidelberg 2002, Heidelberg Dokumenten Server

  7. Helemskii, A.Ya.: The Homology of Banach and Topological Algebras. Dordrecht: Kluwer Academic Publishers, 1989

  8. Karoubi, M.: Formule de Künneth en homologie cyclique I et II. C.R. Acad. Sci. Paris Série A-B 303, 507–510 (1986)

    MATH  Google Scholar 

  9. Kelley, J.L.: General Topology. New York: Van Nostrand, 1955

  10. Kreck, M.: (Co)Homology via Differential topological Varieties. Preprint Mainz, 1999

  11. Kreck, M.: Lecture Notes in Differential Algebraic Topology. Mainz/Heidelberg, 2000

  12. Loday, J.L.: Cyclic homology. Grundlehren der Mathematik, Berlin-Heidelberg-New York: Springer, 1991

  13. Pflaum, M.: Ein Beitrag zur Geometrie und Analysis auf stratifizierten Räumen. Habilitationsschrift, Humboldt Universität Berlin, 2000

  14. Teleman, N.: Microlocalisation de l’homologie de Hochschild. C.R. Acad. Sci. Paris Série 1, 326, 1261–1264 (1998)

    Google Scholar 

  15. Treves, J.F.: Topological Vectorspaces, Distributions and Kernels, London-New-York: Academic Press, 1967

  16. Voigt, J.: Factorization in some Fréchetalgebras of Differentiable Functions, Juergen Voigt, Studia Mathematica, 77, 333–348 (1983)

  17. Weibel, C.: Homological Algebra. Oxford: Oxford University Press, 1995

  18. Wodzicki, M.: Excision in Cyclic Homology, Annals of Math, 129, 591–639 (1989)

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  1. University of Kaiserslautern, Department of Mathematics, 67653, Kaiserslautern, Germany

    Christian-Oliver Ewald

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  1. Christian-Oliver Ewald
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Communicated by A. Connes

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Ewald, CO. Hochschild- and Cyclic-Homology of LCNT-Spaces. Commun. Math. Phys. 250, 195–213 (2004). https://doi.org/10.1007/s00220-004-1149-9

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