Topological complexity of collision-free multi-tasking motion planning on orientable surfaces

TL;DR

This paper calculates the higher topological complexity of configuration spaces on orientable surfaces, extending previous work on their ordinary topological complexity to better understand multi-tasking motion planning.

Contribution

It provides a new computation of the higher topological complexity for configuration spaces on orientable surfaces, expanding the theoretical understanding of motion planning complexity.

Findings

Computed higher topological complexity for configuration spaces on surfaces

Extended Cohen-Farber's results to higher topological complexity

Enhanced understanding of multi-tasking motion planning challenges

Abstract

We compute the higher topological complexity of ordered configuration spaces of orientable surfaces, thus extending Cohen-Farber's description of the ordinary topological complexity of those spaces.