Browsing School of Mathematics, Statistics and Applied Mathematics by Author "Rahm, Alexander D."
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Accessing the cohomology of discrete groups above their virtual cohomological dimension
Rahm, Alexander D. (2014)We introduce a method to explicitly determine the FarrellTate 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 ... 
Cell complexes database for the Bianchi groups
Rahm, Alexander D. (NUI Galway, 20160518)This is a database of quotients by Bianchi groups of twodimensional cellular equivariant retracts of Hyperbolic threespace. The Bianchi groups SL(2, A), with A the ring of integers in the imaginary quadratic number field ... 
Characteristic classes of complexified bundles
Rahm, Alexander D. (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 axioms of ... 
(Co)homologies et Kthéorie de groupes de Bianchi par des modèles géométriques calculatoires
Rahm, Alexander D. (Université de Grenoble / Universität Göttingen, 20101015)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 ... 
Complexifiable characteristic classes
Rahm, Alexander D. (2013) 
Complexifiable characteristic classes
Rahm, Alexander D. (Springer, 201401)We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined. 
Higher torsion in the Abelianization of the full Bianchi groups
Rahm, Alexander D. (Cambridge University Press (Cambridge Journals Online), 201309)Denote by Q(rootm), with m a squarefree positive integer, an imaginary quadratic number field, and by Om its ring of integers. The Bianchi groups are the groups SL2(Om). In the literature, so far there have been no ... 
The homological torsion of PSL_2 of the imaginary quadratic integers
Rahm, Alexander D. (2013)The Bianchi groups are the groups (P)SL2 over a ring of integers in an imaginary quadratic number field. We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which ... 
Homology and Ktheory of the Bianchi groups
Rahm, Alexander D. (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 integral homology of PSL(2) of imaginary quadratic integers with nontrivial class group
Rahm, Alexander D. (2011)We show that a cellular complex defined by Flöge allows us to determine the integral homology of the Bianchi groups PSL(2)(O[m]), where O[m] is the ring of integers of an imaginary quadratic number field Q [square root ... 
The mod 2 cohomology rings of SL2 of the imaginary quadratic integers
Rahm, Alexander D. (Elsevier ScienceDirect, 20150928)We establish general dimension formulae for the second page of the equivariant spectral sequence of the action of the SL2 groups over imaginary quadratic integers on their associated symmetric space. By way of doing this, ... 
On a question of Serre
Rahm, Alexander D. (2012)Consider an imaginary quadratic number field Q(root m), with m a squarefree positive integer, and its ring of integers {O} . The Bianchi groups are the groups SL2{O}. Further consider the BorelSerre compactification [7] ... 
On Level One Cuspidal Bianchi Modular Forms
Rahm, Alexander D. (2013)In this paper, we present the outcome of vast computer calculations, locating several of the very rare instances of level one cuspidal Bianchi modular forms that are not lifts of elliptic modular forms. 
On the equivariant Khomology of PSL_2 of the imaginary quadratic integers
Rahm, Alexander D. (Association des Annales de l'Institut Fourier, 201609)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 numbertheoretic quantities. To achieve this, ... 
A refinement of a conjecture of Quillen
Rahm, Alexander D. (Elsevier ScienceDirect, 201509)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 ... 
The subgroup measuring the defect of the Abelianization of SL_2(Z[i])
Rahm, Alexander D. (Springer, 20130210)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) ...