From wall spaces to CAT(0) cube complexes

We explain how to adapt a construction due to M. Sageev in order to construct a proper action of a group on a CAT(0) cube complex starting from a proper action of the group on a wall space

On the Kropholler conjecture

This short note, produced for the volume of conjectures produced on the occasion of Guido Mislin's retirement, describes the status of the Kropholle conjecture which may be viewed as a far reaching generalisation of Stallings' theorem on groups with more than one end

Some free-by-cyclic groups

We exhibit free-by-cyclic groups containing non-free locally-free subgroups, including some word hyperbolic examples. We also show that these groups are not subgroup separable. We use Bestvina-Brady Morse theory in our arguments

Approximation properties for discrete groups

We give an overview of approximation properties in the context of operator algebras associated with groups

Property A and exactness of the uniform Roe algebra

In this short note, prepared for the volume of conjectures to celebrate Guido Mislin's retirement, we outline the conjecture that a uniformly discrete bounded geometry metric space X has property A if and only if the uniform Roe algebra C^?(X ) is exact