Directed topological complexity of spheres

TL;DR

This paper establishes that the directed topological complexity of the directed n-sphere is consistently 2 for all dimensions n greater than or equal to 1, providing a key insight into the structure of directed spaces.

Contribution

The paper proves that the directed topological complexity of the directed n-sphere is exactly 2 for all n ≥ 1, a new result in directed algebraic topology.

Findings

Directed topological complexity of directed n-spheres is 2 for all n ≥ 1.

Provides a uniform value for the directed topological complexity across all dimensions.

Advances understanding of the complexity of directed topological spaces.

Abstract

We show that the directed topological complexity (as defined by E. Goubault) of the directed $n$-sphere is $2$, for all $n\ge1$.