Perfect forms and the cohomology of modular groups

Abstract

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

17 pages, 7 tables and figures

References in corpus (1)

• Enumerating perfect forms

Cited by in corpus (5)

• Computations in formal symplectic geometry and characteristic classes of moduli spaces
• A stability conjecture for the unstable cohomology of SL_n Z, mapping class groups, and Aut(F_n)
• Stable cohomology of the perfect cone toroidal compactification of ${\mathcal{A}}_g$
• Geometry of theta divisors --- a survey
• On the cohomology of linear groups over imaginary quadratic fields