A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general
construction of many actions of groups on quasi-trees. The groups we can handle include …

Let M be complete nonpositively curved Riemannian manifold of finite volume whose
fundamental group Γ does not contain a finite index subgroup which is a product of infinite …

For every group G, we define the set of hyperbolic structures on G, denoted by ℋ (G), which
consists of equivalence classes of (possibly infinite) generating sets of G such that the …

If G is a group, a pseudocharacter f: G→ ℝ is a function which is “almost” a homomorphism. If
G admits a nontrivial pseudocharacter f, we define the space of ends of G relative to f and …

Tree approximation in quasi-trees Page 1 Groups Geom. Dyn. 17 (2023), 1193–1233 DOI
10.4171/GGD/733 © 2023 European Mathematical Society Published by EMS Press This work …

Using the projection complex machinery, Bestvina-Bromberg-Fujiwara, Hagen-Petyt and
Han-Nguyen-Yang prove that several classes of nonpositively-curved groups admit …

We show that the Lipschitz free space of a countable simplicial quasi-tree is isomorphic to
$\ell^ 1$. As a consequence, every finitely generated group with Property (QT) of Bestvina …

We study the subgroup structure of discrete groups that share cohomological properties
which resemble non-negative curvature. Examples include all Gromov hyperbolic groups …

The study of the poset of hyperbolic structures on a group G was initiated by C. Abbott, S.
Balasubramanya and D. Osin,[Hyperbolic structures on groups, Algebr. Geom. Topol. 19 …

In this monograph we lay the foundation for a theory of coarse groups and coarse actions.
Coarse groups are group objects in the category of coarse spaces, and can be thought of as …