Homotopy index polynomials for knotoids

Igor Nikonov

Homotopy index polynomials for knotoids

Geometric Topology 2026-07-06 v1

Authors: Igor Nikonov

Abstract

We define homotopy index polynomials and a homotopy type of knotoids in an oriented surface, and consider some basic properties of these polynomials. We show that for planar knotoids the homotopy polynomials are not weaker than previously defined index polynomials, and that the homotopy index polynomials detect non-rotatability of spherical knotoids.

Cite

@article{arxiv.2607.04737,
  title  = {Homotopy index polynomials for knotoids},
  author = {Igor Nikonov},
  journal= {arXiv preprint arXiv:2607.04737},
  year   = {2026}
}