Higher topological complexity of planar polygon spaces having small genetic codes

Sutirtha Datta; Navnath Daundkar; Abhishek Sarkar

Higher topological complexity of planar polygon spaces having small genetic codes

Algebraic Topology 2025-09-03 v2

Authors: Sutirtha Datta , Navnath Daundkar , Abhishek Sarkar

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 $km+1.$

Keywords

topological complexity coding theory homotopy groups

Cite

@article{arxiv.2412.01529,
  title  = {Higher topological complexity of planar polygon spaces having small genetic codes},
  author = {Sutirtha Datta and Navnath Daundkar and Abhishek Sarkar},
  journal= {arXiv preprint arXiv:2412.01529},
  year   = {2025}
}

Comments

Accepted for publication in Topology and its Applications. Journal version might slightly differ

Higher topological complexity of planar polygon spaces having small genetic codes

Abstract

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