Classification of tangles - with pictures


If one has a single rope that goes, on the z-axis, from plus infinity
to finite values, is knotted up there, and then continues to
minus infinity, this is probably called a `tangle'.

Is there a classification of such objects? In fact, I'd love to see
one with pictures, but I am not sure such a collection exists.
(Or can one deduce the options from a standard knot table by
cutting? In any case, this is not straightforward, for a
non-mathematician.)

The second issue: Imagine one has *two* such ropes, the
second one going from plus infinity to the knotted part and
continues to minus infinity on (say) the x-axis. Are such
objects classified? (In any case, it is not trivial to map these
objects to links with two components.)

FB

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