  Bonahon-Wong-Yang introduced a new version of the volume conjecture by using
the intertwiners between two isomorphic irreducible representations of the
skein algebra.The intertwiners are built from surface diffeomorphisms; they
made the volume conjecture when diffeomorphisms are pseudo-Anosov. In this
paper we calculated all the intertwiners for the closed torus, producing some
interesting results. Moreover we considered the periodic diffeomorphisms, and
introduced the corresponding conjecture. For some special cases we made precise
calculations for intertwiners and proved our conjecture.

Algebraic Topology;Geometric Topology