Perfect forms and the cohomology of modular groups

Christophe Soul\'e; Herbert Gangl; Philippe Elbaz-Vincent

Perfect forms and the cohomology of modular groups

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arxiv 1001.0789 v1 pith:ZFVSDKEF submitted 2010-01-05 math.NT math.KT

Perfect forms and the cohomology of modular groups

Philippe Elbaz-Vincent , Herbert Gangl , Christophe Soul\'e This is my paper

classification math.NT math.KT

keywords groupscohomologyformsmodularperfectattachedcellclassification

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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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Graph integrals, Feynman periods, and single-valued multiple zeta values
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Canonical integrals of graphs with E=2V−2 equal RW integrals and evaluate to single-valued multiple zeta values, which are shown to lie in the space of Feynman periods.