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http://dx.doi.org/10.4134/BKMS.2012.49.2.395

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

Friedl, Stefan (Mathematisches Institut Universitat zu Koln)
Powell, Mark (Department of Mathematics Indiana University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.2, 2012 , pp. 395-409 More about this Journal
Abstract
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 ${\rightarrow}$ N be a homomorphism between projective $\mathbb{Z}[{\pi}]$-modules such that $\mathbb{Z}_p\;{\otimes}_{\mathbb{Z}[{\pi}]}M{\rightarrow}\mathbb{Z}_p{\otimes}_{\mathbb{Z}[{\pi}]}\;N$ is injective; for which other right $\mathbb{Z}[{\pi}]$-modules V is the induced map $V{\otimes}_{\mathbb{Z}[{\pi}]}\;M{\rightarrow}\;V{\otimes}_{\mathbb{Z}[{\pi}]}\;N$ 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;
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