Geodesic
Acylindrical group actions on quasi-trees
Balasubramanya, Sahana1
1Department of Mathematics, Vanderbilt University, 1326 Stevenson Center Ln, Nashville, TN, 37240, United States
Algebraic and Geometric Topology, Tome 17 (2017) no. 4, pp. 2145-2176
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A group G is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. We prove that every acylindrically hyperbolic group G has a generating set X such that the corresponding Cayley graph Γ is a (non-elementary) quasi-tree and the action of G on Γ is acylindrical. Our proof utilizes the notions of hyperbolically embedded subgroups and projection complexes. As an application, we obtain some new results about hyperbolically embedded subgroups and quasi-convex subgroups of acylindrically hyperbolic groups.

DOI : 10.2140/agt.2017.17.2145
Classification : 20F67, 20F65, 20E08
Keywords: acylindrically hyperbolic groups, acylindrical actions, projection complex, quasi-trees, hyperbolically embedded subgroups

Balasubramanya, Sahana  1

1 Department of Mathematics, Vanderbilt University, 1326 Stevenson Center Ln, Nashville, TN, 37240, United States 
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Balasubramanya, Sahana. Acylindrical group actions on quasi-trees. Algebraic and Geometric Topology, Tome 17 (2017) no. 4, pp. 2145-2176. doi: 10.2140/agt.2017.17.2145

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