Perfect forms and the cohomology of modular groups

Philippe Elbaz-Vincent (1) , Herbert Gangl (2) , Christophe Soulé (3)

1 IF - Institut Fourier
2 Department of Mathematical Sciences, University of Durham
3 IHES - Institut des Hautes Études Scientifiques

For N=5, 6 and 7, using the classification of perfect quadratic forms, we compute the homology of the Voronoï cell complexes attached to the modular groups SL_N(Z) and GL_N(Z). From this we deduce the rational cohomology of those groups.

Keywords: Perfect forms; Voronoï complex; Group cohomology; Modular groups; Machine calculations

Domains: Number Theory [math.NT]; K-Theory and Homology [math.KT]

Philippe Elbaz-Vincent, Herbert Gangl, Christophe Soulé. Perfect forms and the cohomology of modular groups. 2009. ⟨hal-00443899v2⟩