A combination theorem for special cube complexes

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Quasiconvexity and relatively hyperbolic groups that split (2012, background): “n the Bass-Serre tree. Then H is relativelyquasiconvex in G. When the edge groups are separable in G, there is a ﬁnite index subgroup G′ whose splitting has relatively malnormal edge groups (see e.g. [11, 9]). Consequently, if moreover, the edge groups of G are total, then the induced splitting of G”