From CAT(0) to relatively hyperbolic

For zoom details contact Stephan Stadler (stadler@mpim...)

We give a different proof that a CAT(0) Group with isolated flats
is hyperbolic relative to the stabilizers of the maximal flats (first
proven by Hruska  and Kleiner using asymptotic cones).  The approach is
entirely via the boundary and uses the results of Yaman. Along the way we
give  reasonable conditions under which a CAT(0) group acts as a convergence
group on a quotient of its boundary.  We also define the domain of
discontinuity (in the boundary)  of a convex subgroup of a CAT(0) group (on
which the convex subgroup acts properly discontinuous), and give conditions
under which the convex subgroup acts cocompactly on its domain of
discontinuity.