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

DOI10.1016/j.aim.2013.06.014zbMath1290.11104arXiv1001.0789OpenAlexW2062622918MaRDI QIDQ2437488

Philippe Elbaz-Vincent, Herbert Gangl, Christophe Soule

Publication date: 3 March 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.0789

zbMATH Keywords

group cohomologymodular groupSteinberg moduleperfect form\(K\)-theory of integersmachine calculationsVoronoï complex

Mathematics Subject Classification ID

Cohomology of groups (20J06) Equivariant homology and cohomology in algebraic topology (55N91) Structure of modular groups and generalizations; arithmetic groups (11F06) Computations of higher (K)-theory of rings (19D50) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Computational number theory (11Y99) Cohomology of arithmetic groups (11F75) Software, source code, etc. for problems pertaining to manifolds and cell complexes (57-04)

Related Items (17)

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Uses Software

• GAP
• PARI/GP
• PFPK

Cites Work

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• Some computations of the cohomology of \(\text{GL}_N(\mathbb{Z})\) and the \(K\)-theory of \(\mathbb{Z}\)
• The Hurewicz homomorphism in algebraic K-theory
• A spectrum level rank filtration in algebraic \(K\)-theory
• An extension of Tate cohomology to a class of infinite groups
• The cohomology of \(SL_3(Z)\)
• On the torsion in \(K_4(\mathbb{Z})\) and \(K_5(\mathbb{Z})\)
• Die Kohomologie S-arithmetischer Gruppen über Funktionenkörpern
• Computing isometries of lattices
• On the 3-torsion in \(K_4(\mathbb{Z})\)
• Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
• On the cohomology and K-theory of the general linear groups over a finite field
• CLASSES MINIMALES DE RÉSEAUX ET RÉTRACTIONS GÉOMÉTRIQUES ÉQUIVARIANTES DANS LES ESPACES SYMÉTRIQUES
• The complete enumeration of extreme senary forms
• Classification of eight-dimensional perfect forms
• Higher algebraic K-theory: I
• Stable real cohomology of arithmetic groups
• Classification of quintic eutactic forms

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