  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.
