Year: 2024
Type: preprint
Abstract: Link equivalence up to isotopy in a 3-space is the problem that lies at the root of knot theory, and is important in 3-dimensional topology and geometry. We consider its restriction to alternating links, given by two alternating diagrams with $n_1$ and $n_2$ crossings, and show that this problem has polynomial algorithm in terms of $max\{n_1, n_2\}$. For the proof, we use Tait flyping conjectures, observations stemming from the work of Lackenby, Menasco, Sundberg and Thistlethwaite on alternating links, and algorithmic complexity of some problems from graph theory and topological graph theory.
Source: arXiv (Cornell University)
Authors: Haider, Touseef, Tsvietkova, Anastasiia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405035684