Sela proved every torsion-free one-ended hyperbolic group is coHopfian. We
prove that there exist torsion-free one-ended hyperbolic groups that are not
commensurably coHopfian. In particular, we show that the fundamental group of
every simple surface amalgam is not commensurably coHopfian.Comment: v3: 14 pages, 4 figures; minor changes. To appear in International
Mathematics Research Notice
