Let be a word-hyperbolic group, obtained as a graph of free groups amalgamated along cyclic subgroups. If is nonzero, then contains a closed hyperbolic surface subgroup. Moreover, the unit ball of the Gromov–Thurston norm on is a finite-sided rational polyhedron.
"Surface subgroups from homology." Geom. Topol. 12 (4) 1995 - 2007, 2008. https://doi.org/10.2140/gt.2008.12.1995