Higher topological complexity of planar polygon spaces having small genetic codes

Abstract

We study the higher (sequential) topological complexity, a numerical homotopy invariant for the planar polygon spaces. For these spaces with a small genetic codes and dimension m, Davis showed that their topological complexity is either 2m or 2m + 1. We extend these bounds to the setting of higher topological complexity. In particular, when m is power of 2, we show that the k-th higher topological complexity of these spaces is either km or km + 1. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.