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Sur Les Cohomologies de la Formalité Et Les Graphes de Kontsevich

Sur Les Cohomologies de la Formalité Et Les Graphes de Kontsevich

          
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About the Book

Depuis l'article fondateur de Kontsevich, on sait qu'il existe une L∞ formalité pour chaque variété M qui donne une quantification par déformation pour toute structure de Poisson sur M. Dans le cas de R^d, Kontsevich construit une L∞ formalité explicite à l'aide des graphes dits graphes de Kontsevich. Cette thèse développe le calcul de la cohomologie de Chevalley sur ces graphes et précisément des graphes vectoriels et linéaires, à savoir que cette cohomologie est donnée par des graphes à roues de longueur impaire, on retrouve les cocycles fondamentaux de Fuchs et de DeWilde-Lecomte. La cohomologie de Chevalley-Harrison des algèbres de Gerstenhaber est relevant de la structure de G∞ formalité introduite par Tamarkin. On montre que, bien que cette cohomologie est triviale pour l'algèbre T_poly(R^d), le cocycle fondamental de Fuchs survit pour la cohomologie de Chevalley-Harrison à valeurs dans R de l'algèbre de Gerstenhaber T_poly^hom(R^d) formée par des k-tenseurs à coefficients polynomiaux homogènes de degré k. Enfin, on étudie la structure des (a, b)-algèbres qui généralise celle des algèbres de Gerstenhaber et de Poisson graduées et on donne l'algèbre à homotopie près associée.


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Product Details
  • ISBN-13: 9783841785862
  • Publisher: Univ Europeenne
  • Binding: Paperback
  • Language: French
  • Returnable: N
  • Spine Width: 12 mm
  • Width: 152 mm
  • ISBN-10: 3841785867
  • Publisher Date: 28 Feb 2018
  • Height: 229 mm
  • No of Pages: 208
  • Series Title: Omn.Univ.Europ.
  • Weight: 313 gr


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