Quasi-convex Splittings of Acylindrical Graphs of Locally Finite-Height Groups

William D. Cohen

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arXiv · 2503.15459

Quasi-convex Splittings of Acylindrical Graphs of Locally Finite-Height Groups

William D. Cohen

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Abstract

We find a condition on the acylindrical action of a finitely presented group on a simplicial tree which guarantees that this action will be dominated by an acylindrical action with finitely generated edge stabilisers, and find the first example of an action of a finitely presented group where there is no such dominating action. As a consequence, we show that any finitely presented group that admits a decomposition as an acylindrical graph of (possibly infinitely generated) free groups is virtually compact special, and that every finitely generated subgroup of a one-relator group with an acylindrical Magnus hierarchy is virtually compact special.

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BibTeX RIS

William D. Cohen. 2025-03-19. Quasi-convex Splittings of Acylindrical Graphs of Locally Finite-Height Groups. https://arxiv.org/abs/2503.15459

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