Small-dimensional classifying spaces for arithmetic subgroups of general linear groups

DOI10.1215/S0012-7094-84-05123-8zbMath0542.22011OpenAlexW1543007678MaRDI QIDQ795180

Avner Ash

Publication date: 1984

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-84-05123-8

zbMATH Keywords

virtual cohomological dimensioncell-complexnatural compact deformation retract

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Topological (K)-theory (55N15)

Related Items (27)

Modular Forms and Elliptic Curves over the Field of Fifth Roots of Unity ⋮ Cohomology at infinity and the well-rounded retract for general linear groups ⋮ On topologically big divergent trajectories ⋮ On the difficulty of finding spines ⋮ Integral cohomology of certain Picard modular surfaces ⋮ On the integral homology of \(\text{PSL}_4(\mathbb Z)\) and other arithmetic groups ⋮ Minimality of the well-rounded retract. ⋮ On the mod-2 cohomology of \(\mathrm{SL}_3(\mathbb{Z}[\frac{1}{2},i)\)] ⋮ Well-rounded equivariant deformation retracts of Teichmüller spaces ⋮ Dimension rigidity of lattices in semisimple Lie groups ⋮ Computing rational cohomology and Hecke eigenvalues for Bianchi groups ⋮ An explicit spine for the Picard modular group over the Gaussian integers ⋮ Resolutions for unit groups of orders ⋮ Fundamental domains and generators for lattice Veech groups ⋮ Geometry of integral binary Hermitian forms ⋮ Perfect lattices over imaginary quadratic number fields ⋮ Minkowski’s conjecture, well-rounded lattices and topological dimension ⋮ On the cohomology of linear groups over imaginary quadratic fields ⋮ Explicit reduction theory for Siegel modular threefolds ⋮ Lectures on Computing Cohomology of Arithmetic Groups ⋮ On Farrell-Tate cohomology of \(\operatorname{GL}_3\) over rings of quadratic integers ⋮ Integral binary Hamiltonian forms and their waterworlds ⋮ ON THE DIMENSION OF GROUPS THAT SATISFY CERTAIN CONDITIONS ON THEIR FINITE SUBGROUPS ⋮ Computing in arithmetic groups with Voronoï's algorithm. ⋮ Maximal finite subgroups and minimal classes. ⋮ Classical projective geometry and arithmetic groups ⋮ Cohomology of congruence subgroups of \(\text{SL}_4(\mathbb Z)\)

Cites Work

• The integral homology of \(SL_ 2\) and \(PSL_ 2\) of Euclidean imaginary quadratic integers
• Deformation retracts with lowest possible dimension of arithmetic quotients of self-adjoint homogeneous cones
• The cohomology of \(SL_3(Z)\)
• Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
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