2020/10/15 by Craig R. Guilbault, Guilbault, Craig R., Molly A. Moran +1
Mathematics · #20F65 #20J06 #51F30 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2010.08064
openalex publication_date 2020/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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."