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

Title & Authors
AN INJECTIVITY THEOREM FOR CASSON-GORDON TYPE REPRESENTATIONS RELATING TO THE CONCORDANCE OF KNOTS AND LINKS
Friedl, Stefan; Powell, Mark;

Abstract
In the study of homology cobordisms, knot concordance and link concordance, the following technical problem arises frequently: let $\small{{\pi}}$ be a group and let M $\small{{\rightarrow}}$ N be a homomorphism between projective $\small{\mathbb{Z}[{\pi}]}$-modules such that $\small{\mathbb{Z}_p\;{\otimes}_{\mathbb{Z}[{\pi}]}M{\rightarrow}\mathbb{Z}_p{\otimes}_{\mathbb{Z}[{\pi}]}\;N}$ is injective; for which other right $\small{\mathbb{Z}[{\pi}]}$-modules V is the induced map $\small{V{\otimes}_{\mathbb{Z}[{\pi}]}\;M{\rightarrow}\;V{\otimes}_{\mathbb{Z}[{\pi}]}\;N}$ also injective? Our main theorem gives a new criterion which combines and generalizes many previous results.
Keywords
Language
English
Cited by
1.
Whitney towers, gropes and Casson–Gordon style invariants of links, Algebraic & Geometric Topology, 2015, 15, 3, 1813
2.
Links not concordant to the Hopf link, Mathematical Proceedings of the Cambridge Philosophical Society, 2014, 156, 03, 425
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