  We introduce perfect tangles for modular tensor categories. These are
intended to generalise the perfect tensors first introduced in the context of a
toy model for the AdS/CFT correspondence. We construct perfect tangles for
several categories of relevance for topological quantum computation, including
the Temperley-Lieb, Fibonacci, Kuperberg spider, and Haagerup planar algebras.
A general inductive construction proposed by Vaughan Jones for perfect tangles
is also described.
