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Comptes Rendus Mathématique
Volume 335, n° 4
pages 321-324 (2002)
Doi : S1631-073X(02)02481-0
Received : 13 June 2002 ;  accepted : 20 June 2002
Quelques calculs de la cohomologie de GLN(Z) et de la K -théorie de Z
Some computations of the homology of GLN(Z) and the K -theory of Z

Philippe Elbaz-Vincent a , Herbert Gangl b , Christophe Soulé c
a Laboratoire GTA., UMR CNRS 5030, CC51, Université Montpellier II, 34095 Montpellier cedex 5, France 
b MPI für Mathematik Bonn, Vivatsgasse 7, D-53111 Bonn, Allemagne 
c CNRS et IHÉS, 35, route de Chartres, 91440 Bures-sur-Yvette, France 

Note présentée par Jean-Pierre Serre


Pour N =5 et N =6, nous calculons le complexe cellulaire défini par Voronoï à partir des formes quadratiques réelles de dimension N . Nous en déduisons l'homologie de GLN(Z) à coefficients triviaux, à de petits nombres premiers près. Nous montrons aussi que K5(Z)=Z et que K6(Z) n'a que de la 3-torsion. Pour citer cet article : P. Elbaz-Vincent et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 321-324.

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For N =5 and N =6, we compute the Voronoï cell complex attached to real N -dimensional quadratic forms, and we obtain the homology of GLN(Z) with trivial coefficients, up to small primes. We also prove that K5(Z)=Z and K6(Z) has only 3-torsion. To cite this article: P. Elbaz-Vincent et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 321-324.

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© 2002  Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All Rights Reserved.
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