Splittings of groups and intersection numbers

Peter Scott, Gadde A Swarup
2000 Geometry and Topology  
We prove algebraic analogues of the facts that a curve on a surface with self-intersection number zero is homotopic to a cover of a simple curve, and that two simple curves on a surface with intersection number zero can be isotoped to be disjoint.
doi:10.2140/gt.2000.4.179 fatcat:b5mzwopdirdqdh75iqcabyv4lm