For a differentiable knot, i.e. an imbedding
S
n
⊂
S
n
+
2
{S^n} \subset {S^{n + 2}}
, one can associate a sequence of modules
{
A
q
}
\{ {A_q}\}
over the ring
Z
[
t
,
t
−
1
]
Z[t,{t^{ - 1}}]
, which are the source of many classical knot invariants. If X is the complement of the knot, and
X
~
→
X
\tilde X \to X
the canonical infinite cyclic covering, then
A
q
=
H
q
(
X
~
)
{A_q} = {H_q}(\tilde X)
. In this work a complete algebraic characterization of these modules is given, except for the Z-torsion submodule of
A
1
{A_1}
.