$2$-stratifold groups have solvable Word Problem

TL;DR

This paper proves that the word problem for fundamental groups of 2-stratifolds, a generalization of 2-manifolds with complex sheet intersections, is solvable, advancing understanding of their algebraic properties.

Contribution

It establishes the solvability of the word problem for fundamental groups of 2-stratifolds, a significant step in geometric group theory.

Findings

Word problem for 2-stratifold groups is solvable.

Extends known results from 2-manifolds to 2-stratifolds.

Provides a foundation for further algebraic analysis of 2-stratifold groups.

Abstract

$2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where several sheets meet. We show that the word problem for fundamental groups of $2$-stratifolds is solvable.