Models of Simply-connected Trivalent $2$-dimensional Stratifolds with an Implementation Code

Abstract

Trivalent $2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where three sheets meet. We develop operations on their associated labeled graphs that will effectively construct from a single vertex all graphs that represent $1$-connected $2$-stratifolds. We describe an implementation on Python of these operations and other previous results.