A comparison of large scale dimension of a metric space to the dimension of its boundary

Buyalo and Lebedeva have shown that the asymptotic dimension of a hyperbolic group is equal to the dimension of the group boundary plus one. Among the work presented here is a partial extension of that result to all groups admitting ZZ-structures; in particular, we show that asdimG≥dimZ+1asdimG≥dimZ+1 where Z   is the ZZ-boundary.