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

TL;DR

This paper introduces a method to construct and analyze simply-connected trivalent 2-dimensional stratifolds using labeled graphs, with an implementation in Python to facilitate their study.

Contribution

It presents new graph operations for constructing all 1-connected trivalent 2-stratifolds and provides a Python implementation of these methods.

Findings

Effective construction of all 1-connected trivalent 2-stratifolds from a single vertex.

Development of Python code implementing the graph operations.

Enhanced understanding of the structure of trivalent 2-stratifolds.

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.