We introduce and study the notions of hyperbolically embedded and very rotating families of
subgroups. The former notion can be thought of as a generalization of the peripheral …

The key idea in geometric group theory is to study infinite groups by endowing them with a
metric and treating them as geometric spaces. This applies to many groups naturally …

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 …

The theory of bounded cohomology, introduced by Gromov in the late 1980s, has had
powerful applications in geometric group theory and the geometry and topology of …

We provide new examples of acylindrically hyperbolic groups arising from actions on
simplicial trees. In particular, we consider amalgamated products and HNN-extensions, one …

We present some recent rigidity results for von Neumann algebras (II1 factors) and
equivalence relations arising from measure preserving actions of groups on probability …

We study $\epsilon $-representations of discrete groups by unitary operators on a Hilbert
space. We define the notion of Ulam stability of a group which loosely means that finite …

We prove the vanishing of the bounded cohomology of lamplighter groups for a wide range
of coefficients. This implies the same vanishing for a number of groups with self-similarity …

arXiv:1009.0132v1 [math.GR] 1 Sep 2010 Page 1 arXiv:1009.0132v1 [math.GR] 1 Sep 2010
Orbit Equivalence and Measured Group Theory Damien Gaboriau∗ May, 2010 Abstract We …

We determine the bounded cohomology of the group of homeomorphisms of certain low-
dimensional manifolds. In particular, for the group of orientation-preserving …