Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Gügümcü, Neslihan, Kauffman, Louis H.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083683158
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