The number of Simply-connected Trivalent $2$-dimensional Stratifolds

TL;DR

This paper introduces a method to count the number of 1-connected trivalent 2-dimensional stratifolds based on their singular curves and manifold components, advancing understanding of their combinatorial structure.

Contribution

It provides a novel counting method specifically for 1-connected trivalent 2-stratifolds with specified singular and manifold features.

Findings

Developed a counting algorithm for these stratifolds

Derived formulas relating singular curves and components

Enhanced combinatorial classification of 2-stratifolds

Abstract

We describe a method for counting the number of $1$-connected trivalent $2$-stratifolds with a given number of singular curves and $2$-manifold components.