37 citations · 71 across the 14 of their papers we have counts for
16 papers
Arithmetic groups
Vincent Emery
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).
On the systole growth in congruence quaternionic hyperbolic manifolds
Vincent Emery, Inkang Kim, Plinio G. P. Murillo
We provide an explicit lower bound for the sytole in principal congruence covers of compact quaternionic hyperbolic manifolds. We also prove the optimality of this lower bound.
Hyperbolic manifolds and pseudo-arithmeticity
Vincent Emery, Olivier Mila
We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in with . We further show that under an additional assump…
Quaternionic hyperbolic lattices of minimal covolume
Vincent Emery, Inkang Kim
For any n>1 we determine the uniform and nonuniform lattices of the smallest covolume in the Lie group Sp(n,1). We explicitly describe them in terms of the ring of Hurwitz integers…
On volumes of quasi-arithmetic hyperbolic lattices
Vincent Emery
We prove that the covolume of any quasi-arithmetic hyperbolic lattice (a notion that generalizes the definition of arithmetic subgroups) is a rational multiple of the covolume of a…
Salem numbers and arithmetic hyperbolic groups
Vincent Emery, John G. Ratcliffe, Steven T. Tschantz
In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined…
On the torsion part in the K-theory of imaginary quadratic fields
Vincent Emery
We obtain upper bounds for the torsion in the -groups of the ring of integers of imaginary quadratic number fields, in terms of their discriminants.
Hermitian lattices and bounds in K-theory of algebraic integers
Eva Bayer-Fluckiger, Vincent Emery, Julien Houriet
Elaborating on a method of Soulé, and using better estimates for the geometry of hermitian lattices, we improve the upper bounds for the torsion part of the K-theory of the rings o…
Hyperbolic manifolds of small volume
Mikhail Belolipetsky, Vincent Emery
We conjecture that for every dimension n not equal 3 there exists a noncompact hyperbolic n-manifold whose volume is smaller than the volume of any compact hyperbolic n-manifold. F…
On compact hyperbolic manifolds of Euler characteristic two
Vincent Emery
We prove that for n>4 there is no compact arithmetic hyperbolic n-manifold whose Euler characteristic has absolute value equal to 2. In particular, this shows the nonexistence of a…
Torsion homology of arithmetic lattices and K2 of imaginary fields
Vincent Emery
We study upper bounds for the torsion in homology of nonuniform arithmetic lattices. Together with recent results of Calegari-Venkatesh, this can be used to obtain upper bounds on…
The three smallest compact arithmetic hyperbolic 5-orbifolds
Vincent Emery, Ruth Kellerhals
We determine the three hyperbolic 5-orbifolds of smallest volume among compact arithmetic orbifolds, and we identify their fundamental groups with hyperbolic Coxeter groups. This g…
Even unimodular Lorentzian lattices and hyperbolic volume
Vincent Emery
We compute the hyperbolic covolume of the automorphism group of each even unimodular Lorentzian lattice. The result is obtained as a consequence of a previous work with Belolipetsk…
Arbitrarily large families of spaces of the same volume
Vincent Emery
In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume.…
Covolumes of nonuniform lattices in PU(n, 1)
Vincent Emery, Matthew Stover
This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal…
On volumes of arithmetic quotients of PO(n,1), n odd
Mikhail Belolipetsky, Vincent Emery
We determine the minimal volume of arithmetic hyperbolic orientable n-dimensional orbifolds (compact and non-compact) for every odd dimension n>3. Combined with the previously know…