Hyperbolic Coxeter groups with Sierpi\'nski carpet boundary
Jacek \'Swi\k{a}tkowski
TL;DR
This paper characterizes when hyperbolic Coxeter groups with planar nerve have a Sierpiński carpet as their Gromov boundary, providing a complete criterion.
Contribution
It offers a necessary and sufficient condition for hyperbolic Coxeter groups with planar nerve to have a Sierpiński carpet boundary, advancing understanding of their geometric boundaries.
Findings
Identifies conditions for Sierpiński carpet boundary
Provides a complete characterization for hyperbolic Coxeter groups
Enhances understanding of Gromov boundaries in geometric group theory
Abstract
We give a necessary and sufficient condition for a hyperbolic Coxeter group with planar nerve to have Sierpi\'nski curve as its Gromov boundary.
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