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, ...

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 ...

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 ...

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 ...

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) ...

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 ...

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 ...

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.

Consider an imaginary quadratic number field Q(root -m), with m a square-free positive integer, and its ring of integers {O} . The Bianchi groups are the groups SL2{O}. Further consider the Borel-Serre compactification [7] ...