Directed topological complexity of spheres
Ayse Borat, Mark Grant

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 -sphere is , for all .
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