  The theory of bottom tangles is used to construct a quantum fundamental
group. On the other hand, the skein module is considered as a quantum analogue
of the $SL(2)$ representation of the fundamental group. Here we construct the
skein module of a knot complement by using the bottom tangles. We first
construct the universal space of quantum representations, which is a quantum
analogue of the fundamental group, and then factor it by the skein relation to
get the skein module. We also investigate the action of the quantum torus to
the boundary of complement, and derive the recurrence relation of the colored
Jones polynomial, which is known as $A_q$ polynomial.
