Related papers: A note on abelian cubulated groups

For every finite abelian group $G$, there are positive integers $n$ and $d$ such that $G$ is isomorphic to the multiplicative group of $d$-th powers of reduced residues modulo $n$.

H\"older's theorem states that any group acting freely by circle homeomorphisms is abelian, this is no longer true for interval exchange transformations: we first give examples of free actions of non abelian groups. Then after noting that…

We introduce a new kind of action of a relatively hyperbolic group on a CAT(0) cube complex, called a relatively geometric action. We provide an application to characterize finite-volume Kleinian groups in terms of action on cube complexes,…

We define a notion of cofibration among n-categories and show that the cofibrant objects are exactly the free ones, that is those generated by polygraphs.

We show that the affine cactus group is a CAT$(0)$ group for all degrees. Furthermore, we show that the affine cactus group $AJ_3$ of degree three is a hyperbolic group.

Not any nonsingular equation over a metabelian group has solution in a larger metabelian group. However, any nonsingular equation over a solvable group with a subnormal series with abelian torsion-free quotients has a solution in a larger…

The maximal finite abelian subgroups, up to conjugation, of the simple algebraic group of type E8 over an algebraically closed field of characteristic 0 are computed. This is equivalent to the determination of the fine gradings on the…

We give new and improved results on the freeness of subgroups of free profinite groups: A subgroup containing the normal closure of a finite word in the elements of a basis is free; Every infinite index subgroup of a finitely generated…

We provide a necessary and sufficient condition on a finite flag simplicial complex, L, for which there exists a unique CAT(0) cube complex whose vertex links are all isomorphic to L. We then find new examples of such CAT(0) cube complexes…

The primary method for showing that a given cubulated group is hierarchically hyperbolic is by constructing a factor system on the cube complex. In this paper we show that such a construction is not always possible, namely we construct a…

We examine free orientation-reversing group actions on orientable handlebodies, and free actions on nonorientable handlebodies. A classification theorem is obtained, giving the equivalence classes and weak equivalence classes of free…

In this paper we study algebras of modular forms on unitary groups of signature $(n,1)$. We give a necessary and sufficient condition for an algebra of unitary modular forms to be free in terms of the modular Jacobian. As a corollary we…

We provide a systematic description of the automorphism groups of specially cocompact CAT(0) cube complexes. We show that these groups are topologically finitely generated, present a method to explicitly obtain generating sets, and prove a…

Let A be a subset of an abelian group G. We say that A is sum-free if there do not exist x,y and z in A satisfying x + y = z. We determine, for any G, the cardinality of the largest sum-free subset of G. This equals c(G)|G| where c(G) is a…

We use the notion of fixity for representations of finite groups to construct free and smooth actions on products of spheres. In particular we show that a finite p-group (for p>3) will act freely and smoothly on a product of two spheres if…

A (quasi-)Hamiltonian manifold is called multiplicity free if all of its symplectic reductions are 0-dimensional. In this paper, we classify multiplicity free Hamiltonian actions for (twisted) loop groups or, equivalently, multiplicity free…

A description of the derived functors of Lie functors for free abelian groups is given.

In this paper, we study the geometry of cone-offs of CAT(0) cube complexes over a family of combinatorially convex subcomplexes, with an emphasis on their Gromov-hyperbolicity. A first application gives a direct cubical proof of the…

We show that any non abelian free group $\F$ is strongly $\aleph_0$-homogeneous, i.e. that finite tuples of elements which satisfy the same first-order properties are in the same orbit under $\Aut(\F)$. We give a characterization of…

We like to build Abelian groups (or R-modules) which on the one hand are quite free, say $\aleph_{\omega + 1}$-free, and on the other hand, are complicated in suitable sense. We choose as our test problem having no non-trivial homomorphism…