Nicolas Bergeron

The asymptotic growth of torsion homology for arithmetic groups

When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume? We give many examples where this is so, and conjecture precise conditions.

A boundary criterion for cubulation

We give a criterion in terms of the boundary for the existence of a proper cocompact action of a word-hyperbolic group on a

Hyperplane sections in arithmetic hyperbolic manifolds

{\rm CAT}(0)

Torsion homology growth and cycle complexity of arithmetic manifolds

cube complex. We describe applications towards lattices and hyperbolic 3-manifold groups. In particular, by combining the theory of special cube complexes, the surface subgroup result of Kahn-Markovic, and Agols criterion, we find that every subgroup separable closed hyperbolic 3-manifold is virtually fibered.

A Note on Local Rigidity

In this paper, we prove that the homology groups of immersed totally geodesic hypersurfaces of compact arithmetic hyperbolic manifolds virtually inject in the homology group of the

Tetrahedra of flags, volume and homology of SL.3/

Let M be an arithmetic hyperbolic 3-manifold, such as a Bianchi manifold. We conjecture that there is a basis for the second homology of M, where each basis element is represented by a surface of ‘low’ genus, and give evidence for this. We explain the relationship between this conjecture and the study of torsion homology growth.

On the growth of Betti numbers in

The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.

p

In the paper we define a “volume” for simplicial complexes of flag tetrahedra. This generalizes and unifies the classical volume of hyperbolic manifolds and the volume of CR tetrahedral complexes considered in Falbel [6], and Falbel and Wang [8]. We describe when this volume belongs to the Bloch group and more generally describe a variation formula in terms of boundary data. In doing so, we recover and generalize results of Neumann and Zagier [18], Neumann [16] and Kabaya [15]. Our approach is very related to the work of Fock and Goncharov [9; 10]. 57M50; 57N10, 57R20

-adic analytic towers

We study the asymptotic growth of Betti numbers in tower of finite covers and provide simple proofs of approximation results, which were previously obtained by Calegari-Emerton, in the generality of arbitrary p-adic analytic towers of covers. Further, we also obtain partial results about arbitrary pro-

Local Rigidity for -Representations of 3-Manifold Groups

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