87 citations · 292 across the 47 of their papers we have counts for
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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…
Homology and homotopy complexity in negative curvature
Uri Bader, Tsachik Gelander, Roman Sauer
Linear upper bounds are provided for the size of the torsion homology of negatively curved manifolds of finite volume in all dimensions . This extends a classical theorem b…
Counting commensurability classes of hyperbolic manifolds
Tsachik Gelander, Arie Levit
Gromov and Piatetski-Shapiro proved existence of finite volume non-arithmetic hyperbolic manifolds of any given dimension. In dimension four and higher, we show that there are abou…
The generalized Chern conjecture for manifolds that are locally a product of surfaces
Michelle Bucher, Tsachik Gelander
We consider closed manifolds that admit a metric locally isometric to a product of symmetric planes. For such manifolds, we prove that the Euler characteristic is an obstruction to…
Milnor-Wood inequalities for manifolds locally isometric to a product of hyperbolic planes
Michelle Bucher, Tsachik Gelander
This note describes sharp Milnor--Wood inequalities for the Euler number of flat oriented vector bundles over closed Riemannian manifolds locally isometric to products of hyperboli…