Related papers: Profinite rigidity of affine Coxeter groups
We show that all groups in a very large class of Coxeter groups are locally quasiconvex and have uniform membership problem solvable in quadratic time. If a group in the class satisfies a further hypothesis it is subgroup separable and…
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 not true for the Euler characteristic itself and that the…
We show that a profinite group with the same first-order theory as the direct product over all odd primes $p$ of the dihedral group of order $2p$, is necessarily isomorphic to this direct product.
In this paper, which is the continuation of [EFW2], we complete the proof of the quasi-isometric rigidity of Sol and the lamplighter groups. The results were announced in [EFW1].
We study the embedding property in the category of sorted profinite groups. We introduce a notion of the sorted embedding property (SEP), analogous to the embedding property for profinite groups. We show that any sorted profinite group has…
Our aim of this and subsequent papers is to enlighten (a part of, presumably) arithmetic structures of knots. This paper introduces a notion of profinite knots which extends topological knots and shows its various basic properties.…
In a recent paper, Barot and Marsh presented an explicit construction of presentation of a finite Weyl group by any seed of corresponding cluster algebra, i.e. by any diagram mutation-equivalent to an orientation of a Dynkin diagram with…
We prove that finite index subgroups of right angled Artin groups are conjugacy separable. We then apply this result to establish various properties of other classes of groups. In particular, we show that any word hyperbolic Coxeter group…
Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.
We obtain a number of results regarding freeness, quasiconvexity and separability for subgroups of Coxeter groups, Artin groups and one-relator groups with torsion.
We show that sufficiently irreducible Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.
We prove that every word is strongly concise in the class of compact $R$-analytic groups.
We show that fundamental groups of compact, orientable, irreducible 3-manifolds with toroidal boundary are Grothendieck rigid.
We prove that a certain pair of isospectral planar sets are distinguished by torsional rigidity.
We prove that the dual fine Selmer group of an abelian variety over the unramified $\mathbb{Z}_{p}$-extension of a function field is finitely generated over $\mathbb{Z}_{p}$. This is a function field version of a conjecture of…
We show that the "profinite direct sum" is a good notion of infinite direct sums for profinite modules having properties similar to direct sums of abstract modules. For example, the profinite direct sum of projective modules is projective,…
In this note we prove that every non characteristically filiform Lie algebra is endowed with an affine structure.
Let BS(1,n)= < a,b: aba^{-1}=b^n >. We prove that any finitely-generated group quasi-isometric to BS(1,n) is (up to finite groups) isomorphic to BS(1,n). We also show that any uniform group of quasisimilarities of the real line is…
We show that for many right-angled Artin and Coxeter groups, all cocompact cubulations coarsely look the same: they induce the same coarse median structure on the group. These are the first examples of non-hyperbolic groups with this…
We prove that two Artin groups of spherical type are isomorphic if and only if their defining Coxeter graphs are the same.