Une construction du groupe de Fischer
Uniform growth of groups acting on Cartan–Hadamard spaces
In this paper we investigate the growth of finitely generated groups. We recall the definition of the algebraic entropy of a group and show that if the group is acting as a discrete subgroup of the isometry group of a Cartan–Hadamard manifold with pinched negative curvature then a Tits alternative is true. More precisely the group is either virtually nilpotent or has a uniform growth bounded below by an explicit constant.
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Valuations on free resolutions and higher geometric invariants of groups.
Vanishing of the first reduced cohomology with values in an -representation
We prove that the first reduced cohomology with values in a mixing -representation, , vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced -cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced -cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes. We also...
Vanishing theorems and conjectures for the 2-homology of right-angled Coxeter groups.
Veech Groups of Loch Ness Monsters
We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of ) avoiding the set of mappings of norm less than 1 appear as Veech groups of tame non-compact flat surfaces which are Loch Ness monsters. Conversely, a Veech group of any tame flat surface is either countable, or one of three specific types.
Volume of spheres in doubling metric measured spaces and in groups of polynomial growth
Let be a compactly generated locally compact group and let be a compact generating set. We prove that if has polynomial growth, then is a Følner sequence and we give a polynomial estimate of the rate of decay of Our proof uses only two ingredients: the doubling property and a weak geodesic property that we call Property (M). As a matter of fact, the result remains true in a wide class of doubling metric measured spaces including manifolds and graphs. As an application, we obtain a -pointwise...
Volumes of discrete groups and topological complexity of homology spheres.
Weighted -cohomology of Coxeter groups based on barycentric subdivisons.
Word distance on the discrete Heisenberg group
We establish an exact formula for the word distance on the discrete Heisenberg group ℍ₃ with its standard set of generators. This formula is then used to prove the almost connectedness of the spheres for this distance.
-chamber systems, coloured graphs and orbifolds.
Конечные подгруппы гиперболических групп.
О локальной выпуклости функций роста конечно-порожденных групп и вопросе 5.2 из Коуровской тетради.
О рациональных множествах в конечно-порожденных нильпотентных группах
О тригонометриях конечных групп и групп с подгруппами, имеющими тригонометрии
О фундаментальных многоугольниках групп неевклидовой кристаллографии.
Переодические фактор-группы гиперболических групп
Полигонометрии пар групп.
Причесывание треугольных билдингов