Convex Embeddability and Knot Theory
Logic
2025-05-06 v1 Combinatorics
Geometric Topology
Abstract
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of circular orders. These results are then applied to the study of arcs and knots, establishing combinatorial properties and lower bounds (in terms of Borel reducibility) for the complexity of some natural relations between these geometrical objects.
Cite
@article{arxiv.2309.09910,
title = {Convex Embeddability and Knot Theory},
author = {Martina Iannella and Alberto Marcone and Luca Motto Ros and Vadim Weinstein},
journal= {arXiv preprint arXiv:2309.09910},
year = {2025}
}
Comments
46 pages