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Seminar: "Calculating the cohomology of Bianchi groups" (E. Berkove, Lafayette College)

Date: Friday November 28th, 15-16.
Place: CRM, room C1/028
Title: "Calculating the cohomology of Bianchi groups".
Speaker: Ethan Berkove (Lafayette College, USA)

Abstract: Let $\mathcal{O}$ be an imaginary quadratic extension of
the rational  numbers. The Bianchi groups are the matrix groups
$PSL_2(\mathcal{O})$ (or sometimes the corresponding $SL_2$ groups).
In this way, the  Bianchi groups can be thought of as
generalizations of the modular group $PSL_2(\mathbb{Z})$. Bianchi
groups have been studied for over a  century, in fields as varied as
group theory, number theory, and  topology.

In this talk we will provide an introduction to  Bianchi groups and
overview of techniques for calculating their (co)homology.  Many
earlier calculations where done primarily on a case-by-case basis.
Recently, however, Alexander Rahm introduced a cellular space, the
$p$-\textit{torsion subcomplex}, on which the Bianchi groups act.
We will define this complex and describe some recent results of
Alexander Rahm and the speaker which use it.

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