Classification and Models of Simply-connected Trivalent $2$-dimensional   Stratifolds
  Trivalent $2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where three sheets meet. We obtain a classification of $1$-connected $2$-stratifolds in terms of their associated labeled graphs and develop operations that will construct from a single vertex all graphs that represent $1$-connected $2$-stratifolds. 
J.C.G\'omez-Larra\~naga, F.Gonz\'alez-Acu\~na, Wolfgang Heil
math.GT