The \(\ell^2\)-cohomology of hyperplane complements

DOI10.4171/GGD/14zbMath1148.52012arXivmath/0612404MaRDI QIDQ2472585

Tadeusz Januszkiewicz, Michael W. Davis, Ian J. Leary

Publication date: 22 February 2008

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612404

zbMATH Keywords

von Neumann dimensionhyperplane arrangements\(l^2\)-cohomology

Mathematics Subject Classification ID

Relations with arrangements of hyperplanes (32S22) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Exotic index theories on manifolds (58J22) Algebraic topology of manifolds (57N65)

Related Items

Spectral pairs, Alexander modules, and boundary manifolds, Vanishing results for the cohomology of complex toric hyperplane complements, Leray Spectral Sequence for Complements of Certain Arrangements of Smooth Submanifolds, LOCAL SYSTEMS ON COMPLEMENTS OF ARRANGEMENTS OF SMOOTH, COMPLEX ALGEBRAIC HYPERSURFACES, Characteristic varieties of hypersurface complements, \(L ^{2}\)-Betti numbers of plane algebraic curves

Cites Work

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• Arrangements of hyperplanes and Lie algebra homology
• Introduction to \(\ell_2\)-methods in topology: Reduced \(\ell_2\)-homology, harmonic chains, \(\ell_2\)-Betti numbers
• Groupes d'homotopie et classes de groupes abéliens
• THE $\eltwo$-COHOMOLOGY OF ARTIN GROUPS