Related papers: Length functions of 2-dimensional right-angled Art…

We find a condition on the underlying graph of an Artin group that fully determines if it is subgroup separable. As a consequence, an Artin group is subgroup separable if and only if it can be obtained from Artin groups of ranks at most 2…

We generalize the peak-reduction algorithm (Whitehead's theorem) for free groups to a theorem about a general right-angled Artin group A_Gamma. As an application, we find a finite presentation for the automorphism group Aut A_Gamma that…

We initiate the study of affine actions of groups on $\Lambda$-trees for a general ordered abelian group $\Lambda$; these are actions by dilations rather than isometries. This gives a common generalisation of isometric action on a…

We classify simple groups that act by birational transformations on compact complex K\"ahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective…

Bregman and Clay recently characterized which right-angled Artin groups with geometric dimension 2 have vanishing minimal volume entropy. In this note, we extend this characterization to higher dimensions.

We construct and study polyhedral product models for classifying spaces of right-angled Artin and Coxeter groups, general graph product groups and their commutator subgroups. By way of application, we give a criterion of freeness for the…

We classify two-dimensional right-angled Coxeter groups that are quasiisometric to a right-angled Artin group defined by a tree, and show that when this is true the right-angled Coxeter group actually contains a visible finite index…

We show that every group with free $\mathbb{Z}^n$-length function is CAT(0).

Let $G$ be a Lie group acting properly on a smooth manifold $M$. If $M/G$ is connected, then we exhibit some simple and basic constructions for proper actions. In particular, we prove that the reduction principle in compact transformation…

We study groups acting on CAT(0) square complexes. In particular we show if Y is a nonpositively curved (in the sense of A. D. Alexandrov) finite square complex and the vertex links of Y contain no simple loop consisting of five edges, then…

For certain HNN extensions including Baumslag-Solitar groups, a treeing is constructed from their certain probability-measure-preserving actions. This is a treeing of a quotient groupoid of the translation groupoid associated with their…

In 2000, Marc Burger and Shahar Mozes introduced universal groups acting on trees. Such groups provide interesting examples of totally disconnected locally compact groups. Intuitively, these are the largest groups for which all local…

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type…

We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups…

This is the first of two papers in which we investigate the properties of the displacement functions of automorphisms of free groups (more generally, free products) on Culler-Vogtmann Outer space and its simplicial bordification - the free…

We prove that on a metrizable, compact, zero-dimensional space every free action of an amenable group is measurably isomorphic to a minimal $G$-action with the same, i.e. affinely homeomorphic, simplex of measures.

We establish sufficient conditions for the C$^*$-simplicity of two classes of groups. The first class is that of groups acting on trees, such as amalgamated free products, HNN-extensions, and their normal subgroups; for example normal…

We find a polynomial (n^6) isoperimetric function for Artin groups, the defining graph of which contains no edges labelled by 3. This in particular shows that even Artin groups have solvable word problem. We use small cancellation theory of…

We provide upper and lower bounds on the length of the shortest non-trivial element in the derived series and lower central series in the free group on two generators. The techniques are used to provide new estimates on the nilpotent…

Well-known measures of entanglement in one-dimensional many body quantum systems, such as the entanglement entropy and the logarithmic negativity, may be expressed in terms of the correlation functions of local fields known as branch point…