The $F$-polynomial invariant for knotoids
Geometric Topology
2023-12-27 v1
Abstract
As a generalization of the classical knots, knotoids deal with the open ended knot diagrams in a surface. In recent years, many polynomial invariants for knotoids have appeared, such as the bracket polynomial, the index polynomial and the th polynomial, etc. In this paper, we introduce a new polynomial invariant -polynomial for knotoids and discuss some properties of the -polynomial. Then, we construct a family of knotoid diagrams which can be distinguished from each other by the -polynomial but cannnot be distinguished by the index polynomial and the th polynomial.
Cite
@article{arxiv.2312.16058,
title = {The $F$-polynomial invariant for knotoids},
author = {Yi Feng and Fengling Li},
journal= {arXiv preprint arXiv:2312.16058},
year = {2023}
}