대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제49권2호
  • /
  • Pages.395-409
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  • 2012
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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AN INJECTIVITY THEOREM FOR CASSON-GORDON TYPE REPRESENTATIONS RELATING TO THE CONCORDANCE OF KNOTS AND LINKS

  • 투고 : 2010.11.22
  • 발행 : 2012.03.31
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초록

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.

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참고문헌

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피인용 문헌

  1. Whitney towers, gropes and Casson–Gordon style invariants of links vol.15, pp.3, 2015, https://doi.org/10.2140/agt.2015.15.1813
  2. Links not concordant to the Hopf link vol.156, pp.03, 2014, https://doi.org/10.1017/S0305004114000036
  3. Symmetric chain complexes, twisted Blanchfield pairings and knot concordance vol.18, pp.6, 2018, https://doi.org/10.2140/agt.2018.18.3425