AN INJECTIVITY THEOREM FOR CASSON-GORDON TYPE REPRESENTATIONS RELATING TO THE CONCORDANCE OF KNOTS AND LINKS
AN INJECTIVITY THEOREM FOR CASSON-GORDON TYPE REPRESENTATIONS RELATING TO THE CONCORDANCE OF KNOTS AND LINKS
In the study of homology cobordisms, knot concordance and link concordance, the following technical problem arises frequently: let <TEX>${\pi}$</TEX> be a group and let M <TEX>${\rightarrow}$</TEX> N be a homomorphism between projective <TEX>$\mathbb{Z}[{\pi}]$</TEX>-modules such that <TEX>$\mathbb{Z}_p\;{\otimes}_{\mathbb{Z}[{\pi}]}M{\rightarrow}\mathbb{Z}_p{\otimes}_{\mathbb{Z}[{\pi}]}\;N$</TEX> is injective; for which other right <TEX>$\mathbb{Z}[{\pi}]$</TEX>-modules V is the induced map <TEX>$V{\otimes}_{\mathbb{Z}[{\pi}]}\;M{\rightarrow}\;V{\otimes}_{\mathbb{Z}[{\pi}]}\;N$</TEX> also …