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Communications in Mathematical Physics

, Volume 205, Issue 1, pp 53–67 | Cite as

Calcul d'un Invariant de Star-Produit Fermé sur une Variété Symplectique

  • Gilles Halbout
Article

Abstract:

Let M be a symplectic manifold over $ℝ. In [CFS] the authors construct an invariant ϕ in the cyclic cohomology of M for any closed star-product. They compute this invariant in the de Rham complex of M when M=T*V. We generalize this result by computing the image of ϕ in the de Rham complex for any symplectic manifold and any star-product and we show how this invariant is related to the general classification of Kontsevich. The proof uses the Riemann–Roch theorem for periodic cyclic chains of Nest–Tsygan.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Gilles Halbout
    • 1
  1. 1.Institut de Recherche Mathématique Avancée, Université Louis Pasteur, C.N.R.S., 7, rue René Descartes, F-67084 Strasbourg Cedex, France. E-mail: halbout@math.u-strasbg.frFrance

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