Comptes Rendus
no. 4
Quelques calculs de la cohomologie de GL𝐍(ℤ) et de la K-théorie de ℤ
Philippe Elbaz-Vincent1 ; Herbert Gangl2 ; Christophe Soulé3
1 Laboratoire GTA., UMR CNRS 5030, CC51, Université Montpellier II, 34095 Montpellier cedex 5, France
2 MPI für Mathematik Bonn, Vivatsgasse 7, D-53111 Bonn, Allemagne
3 CNRS et IHÉS, 35, route de Chartres, 91440 Bures-sur-Yvette, France
Comptes Rendus. Mathématique, Volume 335 (2002) no. 4, pp. 321-324.

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.

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.

Reçu le :
Accepté le :
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DOI : 10.1016/S1631-073X(02)02481-0

Philippe Elbaz-Vincent 1 ; Herbert Gangl 2 ; Christophe Soulé 3

1 Laboratoire GTA., UMR CNRS 5030, CC51, Université Montpellier II, 34095 Montpellier cedex 5, France
2 MPI für Mathematik Bonn, Vivatsgasse 7, D-53111 Bonn, Allemagne
3 CNRS et IHÉS, 35, route de Chartres, 91440 Bures-sur-Yvette, France 
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Philippe Elbaz-Vincent; Herbert Gangl; Christophe Soulé. Quelques calculs de la cohomologie de $ \mathrm{GL}_{\mathbf{N}}\mathbf{(}\mathbb{Z}\mathbf{)}$ et de la K-théorie de $ \mathbb{Z}$. Comptes Rendus. Mathématique, Volume 335 (2002) no. 4, pp. 321-324. doi : 10.1016/S1631-073X(02)02481-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02481-0/

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