Geodesic
Special cube complexes revisited: a quasi-median generalization
Canadian journal of mathematics, Tome 75 (2023) no. 3, pp. 743-777

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DOI

In this article, we generalize Haglund and Wise’s theory of special cube complexes to groups acting on quasi-median graphs. More precisely, we define special actions on quasi-median graphs, and we show that a group which acts specially on a quasi-median graph with finitely many orbits of vertices must embed as a virtual retract into a graph product of finite extensions of clique-stabilizers. In the second part of the article, we apply the theory to fundamental groups of some graphs of groups called right-angled graphs of groups.
DOI : 10.4153/S0008414X22000141
Mots-clés : quasi-median graphs, graph products of groups, special cube complexes 
Genevois, Anthony. Special cube complexes revisited: a quasi-median generalization. Canadian journal of mathematics, Tome 75 (2023) no. 3, pp. 743-777. doi: 10.4153/S0008414X22000141
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     title = {Special cube complexes revisited: a quasi-median generalization},
     journal = {Canadian journal of mathematics},
     pages = {743--777},
     year = {2023},
     volume = {75},
     number = {3},
     doi = {10.4153/S0008414X22000141},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000141/}
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