Abstract
We generalize Bestvina’s notion of a -boundary for a group to that of a “coarse -boundary”. We show that established theorems about -boundaries carry over nicely to the more general theory, and that some wished-for properties of -boundaries become theorems when applied to coarse -boundaries. Most notably, the property of admitting a coarse -boundary is a pure quasi-isometry invariant. In the process, we streamline both new and existing definitions by introducing the notion of a “model -geometry”. In accordance with the existing theory, we also develop an equivariant version of the above—that of a “coarse -boundary”.
Citation
Craig R. Guilbault. Molly A. Moran. "Coarse -Boundaries for Groups." Michigan Math. J. 73 (4) 693 - 718, August 2023. https://doi.org/10.1307/mmj/20206001
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