2019/09/12 by Enrique Torres-Giese, Torres-Giese, Enrique
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT
paper · pdf · doi:10.48550/arxiv.1909.05924
This version includes a number of corrections
arxiv created 2021/01/22 · arxiv updated 2021/01/25
We define a simpler notion of symmetric topological complexity more ad hoc to the motion planning problem which was the original motivation for the definition of topological complexity. This is a homotopy invariant that we call bidirectional topological complexity. We prove properties of this invariant and show specific instances for which the symmetrized topological complexity can be relaxed to the bidirectional setting. This approach allows us to estimate higher values of symmetrized topological complexities.