Classification and Models of Simply-connected Trivalent $2$-dimensional Stratifolds

J. C. Gómez-Larrañaga, F. González-Acuña, Wolfgang Heil

Published 2016-11-23Version 1

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.