Geodesic
Right-angled Coxeter groups with non-planar boundary
Pallavi Dani1 ; Matthew Haulmark2 ; Genevieve Walsh3
1Louisiana State University, Baton Rouge, USA
2Binghamton University, USA
3Tufts University, Medford, USA
Groups, geometry, and dynamics, Tome 17 (2023) no. 1, pp. 127-155

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DOI

We investigate the planarity of the boundaries of right-angled Coxeter groups. We show that non-planarity of the defining graph does not necessarily imply non-planarity of every boundary of the associated right-angled Coxeter group, although it does in many cases. Our techniques yield a characterization of the triangle-free defining graphs such that the associated right-angled Coxeter group has boundary a Menger curve.
DOI : 10.4171/ggd/668
Classification : 20-XX
Mots-clés : Right-angled Coxeter groups, CAT.0/ geometry, boundaries

Pallavi Dani  1   ; Matthew Haulmark  2   ; Genevieve Walsh  3

1 Louisiana State University, Baton Rouge, USA
2 Binghamton University, USA
3 Tufts University, Medford, USA 
Pallavi Dani; Matthew Haulmark; Genevieve Walsh. Right-angled Coxeter groups with non-planar boundary. Groups, geometry, and dynamics, Tome 17 (2023) no. 1, pp. 127-155. doi: 10.4171/ggd/668
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     title = {Right-angled {Coxeter} groups with non-planar boundary},
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     pages = {127--155},
     year = {2023},
     volume = {17},
     number = {1},
     doi = {10.4171/ggd/668},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/668/}
}
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