Let 
be the space in which a knot 
sits. Then the space "around" the knot, i.e., everything
but the knot itself, is denoted 
and is called the knot complement of 
(Adams 1994, p. 84).
If a knot complement is hyperbolic (in the sense that it admits a complete Riemannian metric of constant Gaussian curvature 
), then this metric is unique (Prasad
1973, Hoste et al. 1998).
Knots." Math. Intell. 20, 33-48,
Fall 1998.Prasad, G. "Stong Rigidity of 
-Rank 1 Lattices." Invent. Math. 21, 255-286,
1973.Rolfsen, D.