Tangle Diagrams
Without loss of generality, consider the marked points on the 3-ball boundary to lie on a great circle. The tangle can be arranged to be in general position with respect to the projection onto the flat disc bounded by the great circle. The projection then gives us a tangle diagram, where we make note of over and undercrossings as with knot diagrams.
Tangles often show up as tangle diagrams in knot or link diagrams and can be used as building blocks for link diagrams, e.g. pretzel links.
Read more about this topic: Tangle Theory
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