Certifying incompressibility of non-injective surfaces with scl
  Cooper-Manning and Louder gave examples of maps of surface groups to PSL(2,C) which are not injective, but are incompressible (i.e. no simple loop is in the kernel). We construct more examples with very simple certificates for their incompressibility arising from the theory of stable commutator length. 
Danny Calegari
math.GR math.GT