Perfect forms and the cohomology of modular groups

Mathematics – Number Theory

Scientific paper

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17 pages, 7 tables and figures

Scientific paper

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.

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