28 citations · 62 across the 15 of their papers we have counts for
22 papers
Benjamini--Schramm convergence of arithmetic locally symmetric spaces
Mikołaj Frączyk, Sebastian Hurtado, Jean Raimbault
We prove that the thin parts of arithmetically defined locally symmetric space take up a negligible part of their volume and deduce asymptotic results on their Betti numbers.
Invariant random subgroups in hyperbolic reflection groups
Jean Raimbault
We prove that the Fuchsian (4,4,4) triangle group and also right-angled reflection groups of hyperbolic spaces in higher dimensions admit ergodic invariant random subgroups having…
Coxeter polytopes and Benjamini--Schramm convergence
Jean Raimbault
We observe that a large part of the volume of a hyperbolic polyhedron is taken by a tubular neighbourhood of its boundary, and use this to give a new proof for the finiteness of ar…
Topological complexity of arithmetic locally symmetric spaces
Mikołaj Frączyk, Sebastian Hurtado, Jean Raimbault
We prove that any arithmetic locally symmetric space is homotopy equivalent to a simplicial complex where the number of simplices is bounded linearly in the volume of the space. Th…
A model for random three--manifolds
Bram Petri, Jean Raimbault
We study compact three-manifolds with boundary obtained by randomly gluing together truncated tetrahedra along their faces. We prove that, asymptotically almost surely as the numbe…
Twisted -torsion on the character variety
Léo Bénard, Jean Raimbault
We define a twisted -torsion on the character variety of 3-manifold and study some of its properties. In the case where is hyperbolic of finite volume, we prove that t…
Profinite invariants of arithmetic groups
Holger Kammeyer, Steffen Kionke, Jean Raimbault +1
We prove that the sign of the Euler characteristic of arithmetic groups with CSP is determined by the profinite completion. In contrast, we construct examples showing that this is…
Betti numbers of Shimura curves and arithmetic three--orbifolds
Mikołaj Frączyk, Jean Raimbault
We show that asymptotically the first Betti number, or the arithmetic genus, of a Shimura curve satisfies the Gauss--Bonnet equality. We also show that the first Betti number of a…
On distinct finite covers of 3-manifolds
Stefan Friedl, JungHwan Park, Bram Petri +2
Every closed orientable surface S has the following property: any two connected covers of S of the same degree are homeomorphic (as spaces). In this, paper we give a complete class…
Subgroup growth of virtually cyclic right-angled Coxeter groups and their free products
Hyungryul Baik, Bram Petri, Jean Raimbault
We determine the asymptotic number of index subgroups in virtually cyclic right-angled Coxeter groups and their free products as .
Subgroup growth of right-angled Artin and Coxeter groups
Hyungryul Baik, Bram Petri, Jean Raimbault
We determine the factorial growth rate of the number of finite index subgroups of right-angled Artin groups as a function of the index. This turns out to depend solely on the indep…
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…
On the torsion in symmetric powers on congruence subgroups of Bianchi groups
Jonathan Pfaff, Jean Raimbault
In this paper we prove that for a fixed neat principal congruence subgroup of a Bianchi group the order of the torsion part of its second cohomology group with coefficients in an i…
On geometric aspects of diffuse groups
Steffen Kionke, Jean Raimbault, Nathan Dunfield
Bowditch introduced the notion of diffuse groups as a geometric variation of the unique product property. We elaborate on various examples and non-examples, keeping the geometric p…
Ends of unimodular random manifolds
Ian Biringer, Jean Raimbault
We study the ends of a generic manifold, with respect to a unimodular measure on the space of pointed Riemannian manifolds with bounded curvatures. We apply our general result to t…
On the convergence of arithmetic orbifolds
Jean Raimbault
We discuss the geometry of some arithmetic orbifolds locally isometric to a product of real hyperbolic spaces of dimension two and three, and prove that certain sequences of non-un…
Analytic, Reidemeister and homological torsion for congruence three--manifolds
Jean Raimbault
Starting from the results in math.DG:1212.3161 we prove that for a given Bianchi group, certain natural coefficent modules and a lot of sequences of congruence subgroups of the siz…
Asymptotics of analytic torsion for hyperbolic three--manifolds
Jean Raimbault
We prove that for certain sequences of hyperbolic three--manifolds with cusps which converge to hyperbolic three--space in a weak ("Benjamini-Schramm") sense and certain coefficien…
On the growth of -invariants for sequences of lattices in Lie groups
Miklos Abert, Nicolas Bergeron, Ian Biringer +4
We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of…
A note on maximal lattice growth in SO(1,n)
Jean Raimbault
We show that the number of noncommensurable lattices, hence also that of maximal lattices in SO(1,n) is at least exponential. To do so we construct large families of noncommensurab…
On the growth of Betti numbers of locally symmetric spaces
Miklos Abert, Nicolas Bergeron, Ian Biringer +4
We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uni…
Exponential growth of torsion in Abelian coverings
Jean Raimbault
We study the growth of the order of torsion subgroups of the homology in a tower of finite abelian coverings. In particular, we prove that it is exponential for when the tower conv…