  In this paper a class of multi-Chern-Simons field theories which is relevant
to the statistical mechanics of polymer systems is investigated. Motivated by
the problems which one encounters in the treatment of these theories, a general
procedure is presented to eliminate the Chern-Simons fields from their action.
In this way it has been possible to derive an expression of the partition
function of topologically linked polymers which depends explicitly on the
topological numbers and does not have intractable nonlocal terms as it happened
in previous approaches. The new formulation of multi-Chern-Simons field
theories is then used to remove and clarify some inconsistencies and
ambiguities which apparently affect field theoretical models of topologically
linked polymers. Finally, the limit of disentangled polymers is discussed.
