English

The Mock Alexander Polynomial for Knotoids and Linkoids

Geometric Topology 2024-06-13 v1

Abstract

The mock Alexander polynomial is an extension of the classical Alexander polynomial, defined and studied for (virtual) knots and knotoids by the second and third authors. In this paper we consider the mock Alexander polynomial for generalizations of knotoids. We prove a conjecture on the mock Alexander polynomial for knotoids, which generalizes to uni-linkoids. Afterwards we give constructions for canonical invariants of linkoids derived from the mock Alexander polynomial, using the formalism of generalized knotoids due to Adams et al.

Keywords

Cite

@article{arxiv.2406.08253,
  title  = {The Mock Alexander Polynomial for Knotoids and Linkoids},
  author = {Joanna A. Ellis-Monaghan and Neslihan Gügümcü and Louis H. Kauffman and Wout Moltmaker},
  journal= {arXiv preprint arXiv:2406.08253},
  year   = {2024}
}

Comments

26 pages, 26 figures, comments are welcome

R2 v1 2026-06-28T17:03:10.771Z