38 citations · 102 across the 18 of their papers we have counts for
7 papers · 1 filter
On homology torsion growth
Miklos Abert, Nicolas Bergeron, Mikolaj Fraczyk +1
We prove new vanishing results on the growth of higher torsion homologies for suitable arithmetic lattices, Artin groups and mapping class groups. The growth is understood along Fa…
Convergence of normalized Betti numbers in nonpositive curvature
Miklos Abert, Nicolas Bergeron, Ian Biringer +1
We study the convergence of volume-normalized Betti numbers in Benjamini-Schramm convergent sequences of non-positively curved manifolds with finite volume. In particular, we show…
On the growth of L2-invariants of locally symmetric spaces, II: exotic invariant random subgroups in rank one
Miklos Abert, Nicolas Bergeron, Ian Biringer +4
In the first paper of this series (arxiv.org/abs/1210.2961) we studied the asymptotic behavior of Betti numbers, twisted torsion and other spectral invariants for sequences of latt…
Local rigidity for PGL(3,C)-representations of 3-manifold groups
N. Bergeron, E. Falbel, A. Guilloux +2
Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by…
On the growth of Betti numbers in -adic analytic towers
Nicolas Bergeron, Peter Linnell, Wolfgang Lück +1
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…
Tetrahedra of flags, volume and homology of SL(3)
Nicolas Bergeron, Elisha Falbel, Antonin Guilloux Antonin
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 tetrah…
A boundary criterion for cubulation
Nicolas Bergeron, Daniel T. Wise
We give a criterion in terms of the boundary for the existence of a proper cocompact action of a word-hyperbolic group on a CAT(0) cube complex. We describe applications towards la…