Groups, Geometry, and Dynamics


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Published online first: 2021-07-23
DOI: 10.4171/GGD/611

Entropy and finiteness of groups with acylindrical splittings

Filippo Cerocchi[1] and Andrea Sambusetti[2]

(1) Università di Roma La Sapienza, Roma, Italy
(2) Università di Roma La Sapienza, Roma, Italy

We prove that there exists a positive, explicit function $F(k, E)$ such that, for any group $G$ admitting a $k$-acylindrical splitting and any generating set $S$ of $G$ with $\operatorname{Ent}$(G,S)

Keywords: Acylindrical splittings, entropy, Gromov hyperbolic spaces, CAT(0)-spaces, 2-dimensional orbifolds, 3-manifolds, ramified coverings, high dimensional graph manifolds.

Cerocchi Filippo, Sambusetti Andrea: Entropy and finiteness of groups with acylindrical splittings. Groups Geom. Dyn. Electronically published on July 23, 2021. doi: 10.4171/GGD/611 (to appear in print)