  By applying a variant of the TQFT constructed by Blanchet, Habegger, Masbaum,
and Vogel, and using a construction of Ohtsuki, we define a module endomorphism
for each knot K by using a tangle obtained from a surgery presentation of K. We
show that it is strong shift equivalent to the Turaev-Viro endomorphism
associated to K. Following Viro, we consider the endomorphisms that one obtains
after coloring the meridian and longitude of the knot. We show that the traces
of these endomorphisms encode the same information as the colored Jones
polynomials of K at a root of unity. Most of the discussion is carried out in
the more general setting of infinite cyclic covers of 3-manifolds.
