Bulletin of the
Korean Mathematical Society BKMS

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 $\mathbb Z[\pi]$-modules such that $\mathbb Z_p \otimes_{\mathbb Z[\pi]} M\to \mathbb Z_p \otimes_{\mathbb Z[\pi]} N$ is injective; for which other right $\mathbb Z[\pi]$-modules $V$ is the induced map $V \otimes_{\mathbb Z[\pi]} M\to V\otimes_{\mathbb Z[\pi]}N$ also injective? Our main theorem gives a new criterion which combines and generalizes many previous results.

Keywords: knot concordance, link concordance, $p$ groups, injectivity theorem

MSC numbers: 57M25, 20J05