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arXiv · 2309.09910

Convex Embeddability and Knot Theory

Martina Iannella·Alberto Marcone·Luca Motto Ros·Vadim Weinstein
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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.

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Martina Iannella, Alberto Marcone, Luca Motto Ros, Vadim Weinstein. 2023-09-18. Convex Embeddability and Knot Theory. https://doi.org/10.1090/tran%2F9334

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