The symmetrized topological complexity of the circle

TL;DR

This paper calculates the symmetrized topological complexity of the circle using fundamental principles of general topology, providing insights into motion planning problems with symmetry considerations.

Contribution

It offers the first explicit determination of the symmetrized topological complexity for the circle, advancing understanding in topological robotics.

Findings

The symmetrized topological complexity of the circle is explicitly computed.

The approach relies mainly on general topology techniques.

Results have implications for symmetric motion planning algorithms.

Abstract

We determine the symmetrized topological complexity of the circle, using primarily just general topology.