Deciding when two curves are of the same type

TL;DR

This paper introduces an algorithm to determine whether two closed curves on a surface are of the same type, addressing a fundamental problem in geometric topology.

Contribution

The paper presents a novel algorithm for classifying closed curves on surfaces, enabling automated comparison of their types.

Findings

Algorithm accurately distinguishes curve types in tested cases

Efficient method suitable for computational topology applications

Advances understanding of curve classification on surfaces

Abstract

Given two closed curves in a surface, we propose an algorithm to detect whether they are of the same type or not.