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In the study of homology cobordisms, knot concordance and link concordance,the following technical problem arises frequently: let $\pi$ be a group and let$M \to N$ be a homomorphism between projective $\Z[\pi]$-modules such that$\Z_p \otimes_{\Z[\pi]} M\to \Z_p \otimes_{\Z[\pi]} N$ is injective; for whichother right $\Z[\pi]$-modules $V$ is the induced map $V \otimes_{\Z[\pi]} M\toV\otimes_{\Z[\pi]}N$ also injective? Our main theorem gives a new criterionwhich combines and generalizes many previous results.

AN INJECTIVITY THEOREM FOR CASSON-GORDON TYPE REPRESENTATIONS RELATING TO THE CONCORDANCE OF KNOTS AND LINKS