Right-angled Artin groups with non-path-connected boundary
Wes Camp
TL;DR
This paper identifies specific conditions on the presentation graph of right-angled Artin groups that ensure their associated CAT(0) cube complex has a boundary that is not path-connected.
Contribution
It provides new criteria linking the presentation graph of right-angled Artin groups to the topological properties of their CAT(0) boundaries.
Findings
Certain graph conditions lead to non-path-connected boundaries.
The paper characterizes when the boundary of the cube complex is disconnected.
Results connect graph properties to geometric boundary topology.
Abstract
We place conditions on the presentation graph of a right-angled Artin group that guarantee the standard CAT(0) cube complex on which the group acts geometrically has non-path-connected boundary.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models