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Convex Embeddability and Knot Theory

Martina IannellaAlberto MarconeLuca Motto RosVadim Weinstein
Sep 2023
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摘要原文
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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