The clock theorem for knotoids and linkoids

Neslihan Gügümcü; Louis H. Kauffman

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arXiv · 2509.21568

The clock theorem for knotoids and linkoids

Neslihan Gügümcü·Louis H. Kauffman

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Abstract

In this paper, we generalize the \textit{Clock Theorem} of Formal Knot Theory to knotoids in $S^2$. The clock theorem implies that clock states of a knotoid diagram form a lattice under transpositions. These states form the basis of many invariants of knotoids and linkoids including the Alexander polynomial, Mock Alexander polynomial and the Jones polynomial.

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Neslihan Gügümcü, Louis H. Kauffman. 2025-09-25. The clock theorem for knotoids and linkoids. https://arxiv.org/abs/2509.21568

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