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Quasi-convex Splittings of Acylindrical Graphs of Locally Finite-Height Groups by Cohen, William D. is a scholarly article available to read on EtoBox.

What is Quasi-convex Splittings of Acylindrical Graphs of Locally Finite-Height Groups about?

We find a condition on the 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 hyperbolic group that admits a decomposition as an acylindrical graph of (possibly infinitely generated) free groups is virtually cocompact special, and that if one assumes that every finite-height subgroup of a hyperbolic group is quasi-convex then every finitely generated subgroup of a one-relator group with an acylindrical Magnus hierarchy admits a quasi-convex hierarchy.

Author

Cohen, William D.

Published

2025

Language

EN