Perfect forms, K-theory and the cohomology of modular groups

By Philippe Elbaz-Vincent, Herbert Gangl, Christophe Soulé. 2013

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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 G L N ( Z ) . From this we deduce the rational cohomology of those groups and some information about K m ( Z ) , when m = 5 , 6 and 7.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/994a2f804bbe315fdc45a9b876b2df13c168bbea