Related papers: Embedding Partial HNN Extensions In Ascending HNN …

A geometric extension algebra is an extension algebra of a semi-simple perverse sheaf (allowing shifts), e.g. a push-forward of the constant sheaf under a projective map. Particular nice situations arise for collapsings of homogeneous…

In this paper we identify different classes of free group extension using core graphs. We show that every free group extension $H\leq K\leq F$ has a base $B$ such that the associated pointed graph morphism…

Natural language text exhibits hierarchical structure in a variety of respects. Ideally, we could incorporate our prior knowledge of this hierarchical structure into unsupervised learning algorithms that work on text data. Recent work by…

In this paper we describe finitely generated groups $H$ universally equivalent (with constants from $G$ in the language) to a given torsion-free relatively hyperbolic group $G$ with free abelian parabolics. It turns out that, as in the free…

We give a counterexample to a conjecture by Miasnikov, Ventura and Weil, stating that an extension of free groups is algebraic if and only if the corresponding morphism of their core graphs is onto, for every basis of the ambient group. In…

In this paper, we prove that infinite cancellative finitely generated hyperbolic monoids never contain $\mathbb N\times\mathbb N$ as a submonoid but that they contain an element of infinite order and, if they are elementary, then they also…

We show that there exist finitely generated soluble groups which are not LERF but which do not contain strictly ascending HNN extensions of a cyclic group. This solves Problem 16.2 in the Kourovka notebook. We further show that there is a…

We prove that, if a group is relatively hyperbolic, the parabolic subgroups are virtually nilpotent if and only if there exists a hyperbolic space with bounded geometry on which it acts geometrically finitely. This provides, by use of M.…

We study relations between maps between relatively hyperbolic groups/spaces and quasisymmetric embeddings between their boundaries. More specifically, we establish a correspondence between (not necessarily coarsely surjective)…

We construct the HNN extension of discrete quantum groups, we study their representation theory and we show that an HNN extension of amenable discrete quantum groups is K-amenable.

Binary Neural Network (BNN) converts full-precision weights and activations into their extreme 1-bit counterparts, making it particularly suitable for deployment on lightweight mobile devices. While binary neural networks are typically…

We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the…

We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$. This construction…

We prove the following version of Milnor's theorem on solvable groups of exponential growth: A finitely generated solvable group which is not polycyclic contains an ascending HNN extension. Consequently, a finitely generated solvable group…

We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface…

This is the second part of a two part work in which we prove that for every finitely generated subgroup $\Gamma < \mathsf{Out}(F_n)$, either $\Gamma$ is virtually abelian or its second bounded cohomology $H^2_b(\Gamma;\mathbb{R})$ contains…

We study the second bounded cohomology of an amalgamated free product of groups, and an HNN extension of a group. As an application, we have a group with infinitely many ends has infinite dimensional second bounded cohomology.

A group $G$ is said to have the Howson property (or to be a Howson group) if the intersection of any two finitely generated subgroups of $G$ is finitely generated subgroup. It is proved that descending HNN-extension is not a Howson group…

We build quasi--isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previously introduced by the authors. We prove that, given any…

We use algebraic techniques to study homological filling functions of groups and their subgroups. If $G$ is a group admitting a finite $(n+1)$--dimensional $K(G,1)$ and $H \leq G$ is of type $F_{n+1}$, then the $n^{th}$--homological filling…