Quelques calculs de la cohomologie de GL_N(Z) et de la K-theorie de Z, by Philippe Elbaz-Vincent, Herbert Gangl, and Christophe Soule

For N=5 and N=6, we compute the Voronoi cell complex attached to real N-dimensional quadratic forms, and we obtain the homology of GL_N(Z) with trivial coefficients, up to small primes. We also prove that K_5(Z) = Z and K_6(Z) has only 3-torsion.

Keywords: K-theory; Arithmetic groups; Perfect forms; Reduction theory of quadratic forms.

Philippe Elbaz-Vincent <pev@math.univ-montp2.fr>
Herbert Gangl <herbert@mpim-bonn.mpg.de>
Christophe Soule <soule@ihes.fr>