UNRAVELING THE INTEGRAL KNOT CONCORDANCE GROUP 15

isometric structures annihilated by T . An important special case will

be when T consists of non-negative powers of a fixed polynomial c p ,

abusing notation, we will denote this case by C„„(R) .

b) Let S be and R-algebra, finitely generated as an R-module.

Then C (R) will denote the concordance classes of isometric structures

which have a compatible S-module structure, that is there is an element

s in S so that sx = t(x) for all x in the underlying module M .

The correct usage of the subscript will always be clear from the context.

We now extend the injection C" (2S)~ * C (Q) to a short exact

sequence in order to further understand the structure of the integral

concordance group.