Quasi-isometries need not induce homeomorphisms of contracting boundaries with the Gromov product topology

DOI10.1515/AGMS-2016-0011zbMath1377.20030arXiv1605.01660OpenAlexW2497556386MaRDI QIDQ311228

Christopher H. Cashen

Publication date: 29 September 2016

Published in: Analysis and Geometry in Metric Spaces (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.01660

zbMATH Keywords

quasi-isometryGromov boundary\(\mathrm{CAT}(0)\) spacegeodesic spacescontracting boundary

Mathematics Subject Classification ID

Geometric group theory (20F65) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Topological methods in group theory (57M07) Geodesics in global differential geometry (53C22) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (4)

Sublinearly Morse boundary. I: CAT(0) spaces ⋮ Right-angled Coxeter groups with totally disconnected Morse boundaries ⋮ Comparing topologies on the Morse boundary and quasi-isometry invariance ⋮ A metrizable topology on the contracting boundary of a group

Cites Work

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• Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction
• Morse boundaries of proper geodesic metric spaces
• Spaces with nonpositive curvature and their ideal boundaries
• Hyperbolic quasi-geodesics in CAT(0) spaces.
• Comparing the Floyd and ideal boundaries of a metric space
• Contracting boundaries of CAT(0) spaces

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