We use an accessibility result of Delzant and Potyagailo to prove Swarup’s Strong Accessibility Conjecture for Gromov hyperbolic groups with no –torsion. It follows that, if is an irreducible, orientable, compact –manifold with hyperbolic fundamental group, then any hierarchy in which is decomposed alternately along compressing disks and essential annuli is finite.
"Strong accessibility for hyperbolic groups." Algebr. Geom. Topol. 8 (3) 1459 - 1479, 2008. https://doi.org/10.2140/agt.2008.8.1459