
In this talk, I would like to expose current situation of the volume
conjecture. This conjecture gives a relation on a knot between the volume
of its complement and its quantum invariants. Such astonishing relation
was first discovered by R. M. Kashaev for several hyperbolic knots, and
many evidences were given after that. Especially, Y. Yokota showed an
actual relation between the volume conjecture and the hyperbolic structure,
which is a good approval for the conjecture. A quick review for knot
complement case is given, and generalization to 3manifolds is also
discussed.
