Gromov hyperbolic groups and the Macaev norm. (Q868744)

Let \(\Gamma\) be a Gromov hyperbolic group with a finite set \(A\) of generators. One can consider three quantities: the Coornaert-Papadopoulos topological entropy \(h_{top}(\Sigma(\infty))\) of the subshift associated to \((\Gamma,A)\), Voiculescu's invariant \(k^-_\infty(\lambda_A)\), and the growth entropy \(\text{gr}(\Gamma,A)\). The author proves that \(h_{top}(\Sigma(\infty))\leq k^-_\infty(\lambda_A)\leq\text{gr}(\Gamma,A)\) and that these invariants are equal for a hyperbolic group splitting over a finite group.