Volume conjecture

Volume conjecture
Field	Knot theory
Conjectured by	Hitoshi Murakami; Jun Murakami; Rinat Kashaev;
Known cases	figure-eight knot; three-twist knot; Borromean rings; torus knots; all knots and links with volume zero; twisted Whitehead links; Whitehead doubles of nontrivial torus knots with ;
Consequences	Vassiliev invariants detect the unknot

In the branch of mathematics called knot theory, the volume conjecture is an open problem that relates quantum invariants of knots to the hyperbolic geometry of their complements.