TL;DR
This paper characterizes which groups can act geometrically on CAT(0) spaces with boundaries homeomorphic to a circle or a suspension of a Cantor set, providing a precise classification based on boundary topology.
Contribution
It precisely determines the groups that admit geometric actions on CAT(0) spaces with specific boundary topologies, namely circle or suspension of a Cantor set.
Findings
Groups acting on CAT(0) spaces with circle boundary are classified.
Groups acting on CAT(0) spaces with suspension of Cantor set boundary are characterized.
The boundary topology constrains the algebraic structure of the acting groups.
Abstract
We specify exactly which groups can act geometrically on CAT(0) spaces whose visual boundary is homeomorphic to either a circle or a suspension of a Cantor set.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory