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On the equivariant K-homology of PSL_2 of the imaginary quadratic integers
(Association des Annales de l'Institut Fourier, 2016-09)
We establish formulae for the part due to torsion of the equivariant $K$-homology of all the Bianchi groups (PSL$_2$ of the imaginary quadratic integers), in terms of elementary number-theoretic quantities. To achieve this, ...
A refinement of a conjecture of Quillen
(Elsevier ScienceDirect, 2015-09)
We present some new results on the cohomology of a large scope of SL2 groups in degrees above the virtual cohomological dimension, yielding some partial positive results for the Quillen conjecture in rank one. We combine ...
Cell complexes database for the Bianchi groups
(NUI Galway, 2016-05-18)
This is a database of quotients by Bianchi groups of two-dimensional cellular equivariant retracts of Hyperbolic three-space. The Bianchi groups SL(2, A), with A the ring of integers in the imaginary quadratic number field ...
Accessing the cohomology of discrete groups above their virtual cohomological dimension
(2014)
We introduce a method to explicitly determine the Farrell-Tate cohomology of discrete groups. We apply this method to the Coxeter triangle and tetrahedral groups as well as to the Bianchi groups, i.e. PSL_2 over the ring ...
Homology and K-theory of the Bianchi groups
(2011)
We reveal a correspondence between the homological torsion of the Bianchi groups
and new geometric invariants, which are effectively computable thanks to their
action on hyperbolic space. We use it to explicitly compute ...
The subgroup measuring the defect of the Abelianization of SL_2(Z[i])
(Springer, 2013-02-10)
There is a natural inclusion of SL2(Z) into SL2(Z[i]) , but it does not induce an injection of commutator factor groups (Abelianizations). In order to see where and how the 3 -torsion of the Abelianization of SL2(Z) ...
Higher torsion in the Abelianization of the full Bianchi groups
(Cambridge University Press (Cambridge Journals Online), 2013-09)
Denote by Q(root-m), with m a square-free positive integer, an imaginary quadratic number field, and by O-m its ring of integers. The Bianchi groups are the groups SL2(O-m). In the literature, so far there have been no ...
(Co)homologies et K-théorie de groupes de Bianchi par des modèles géométriques calculatoires
(Université de Grenoble / Universität Göttingen, 2010-10-15)
Cette thèse consiste d'une étude de la géométrie d'une certaine classe de groupes arithmétiques, à travers d'une action propre sur un espace contractile. Nous calculons explicitement leur homologie de groupe, et leur ...
Characteristic classes of complexified bundles
(Summer School in Algebraic Topology: Sheaf theoretic methods in the theory of characteristic classes, 2007)
We examine the topological characteristic cohomology classes of complexified vector bundles . In particular, all the classes coming from real vector bundles are computed. We use characteristic classes with the ax-ioms of ...