The homological torsion of PSL$_2$ of the imaginary quadratic integers

DOI10.1090/S0002-9947-2012-05690-XzbMath1307.11065arXiv1108.4608OpenAlexW2064204656MaRDI QIDQ4913822

Alexander D. Rahm

Publication date: 16 April 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.4608

Mathematics Subject Classification ID

Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Equivariant homology and cohomology in algebraic topology (55N91) Discrete subgroups of Lie groups (22E40) Discontinuous groups of transformations (57S30) Equivariant (K)-theory (19L47) Cohomology of arithmetic groups (11F75)

Related Items

The homology of \(SL_2\) of discrete valuation rings, Homology of \(\operatorname{SL}_2\) over function fields. I: Parabolic subcomplexes, On Farrell-Tate cohomology of \(\mathrm{SL}_2\) over \(S\)-integers, The mod 2 cohomology rings of \(\mathrm{SL}_2\) of the imaginary quadratic integers. With an appendix by Aurel Page, Accessing the cohomology of discrete groups above their virtual cohomological dimension, Computing Bredon homology of groups, On the equivariant \(K\)-homology of \(\mathrm{PSL}_2\) of the imaginary quadratic integers, Higher torsion in the Abelianization of the full Bianchi groups, The subgroup measuring the defect of the Abelianization of \(\mathrm{SL}_2(\mathbb Z[i)\).], The mod 2 cohomology rings of congruence subgroups in the Bianchi groups, On Ruan's cohomological crepant resolution conjecture for the complexified Bianchi orbifolds, On the cohomology of linear groups over imaginary quadratic fields, Maximal finite subgroups and minimal classes.

Uses Software

• PARI/GP
• Bianchi.gp

Cites Work

• The integral homology of \(\mathrm{PSL}_2\) of imaginary quadratic integers with nontrivial class group
• Homology and \(K\)-theory of the Bianchi groups.
• The integral homology of \(SL_ 2\) and \(PSL_ 2\) of Euclidean imaginary quadratic integers
• Rational homology of Bianchi groups
• Zur Struktur der \(\mathrm{PSL}_2 \) über einigen imaginär-quadratischen Zahlringen
• Deformation retracts with lowest possible dimension of arithmetic quotients of self-adjoint homogeneous cones
• Modular symbols for \(\mathbb{Q}\)-rank one groups and Voronoĭ reduction
• Bredon homology and equivariant \(K\)-homology of \(\mathrm{SL}(3,\mathbb Z)\)
• Generators and relations for certain special linear groups
• Foundations of Hyperbolic Manifolds
• Periods of Cusp Forms and Elliptic Curves Over Imaginary Quadratic Fields
• The Mod-2 cohomology of the Bianchi groups
• On the Integral Cohomology of Bianchi Groups
• Hyperbolic Tessellations Associated to Bianchi Groups
• Finding All Elliptic Curves with Good Reduction Outside a Given Set of Primes
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