Croke-Kleiner admissible groups: Property (QT) and quasiconvexity

Abstract

Croke-Kleiner admissible groups firstly introduced by Croke-Kleiner belong to a particular class of graph of groups which generalize fundamental groups of $3$--dimensional graph manifolds. In this paper, we show that if $G$ is a Croke-Kleiner admissible group, acting geometrically on a CAT(0) space $X$, then a finitely generated subgroup of $G$ has finite height if and only if it is strongly quasi-convex. We also show that if $G\curvearrowright X$ is a flip CKA action then $G$ is quasi-isometric embedded into a finite product of quasi-trees. With further assumption on the vertex groups of the flip CKA action $G\curvearrowright X$, we show that $G$ satisfies property (QT) that is introduced by Bestvina-Bromberg-Fujiwara.

We fix some gaps in Section 5 of the previous version. The main results are not affected

References in corpus (1)

• Quasiconvexity in $3$-manifold groups

Cited by in corpus (2)

• Property (QT) for 3-manifold groups
• Almost invariant CND kernels and proper uniformly Lipschitz actions on subspaces of $L^1$