Coarse Z-Boundaries for Groups

We generalize Bestvina's notion of a Z-boundary for a group to that of a "coarse Z-boundary". We show that established theorems about Z-boundaries carry over nicely to the more general theory, and that some wished-for properties of Z-boundaries become theorems when applied to coarse Z-boundaries. Most notably, the property of admitting a coarse Z-boundary is a pure quasi-isometry invariant. In the process, we streamline both new and existing definitions by introducing the notion of a "model Z-geometry". In accordance with the existing theory, we also develop an equivariant version of the above-that of a "coarse EZ-boundary".