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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Elementary surgery manifolds and the elementary ideals


Author: J. P. Neuzil
Journal: Proc. Amer. Math. Soc. 68 (1978), 225-228
MSC: Primary 55A25; Secondary 57A10
MathSciNet review: 0464216
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Abstract: We prove the following: If $ {M^3}$ is a closed 3-manifold obtained by elementary surgery on a knot K in $ {S^3}$ and $ {H_1}({M^3})$ is a nontrivial cyclic group, then the first elementary ideal $ {\pi _1}({M^3})$ in the integral group ring of $ {H_1}({M^3})$ is the principal ideal generated by the polynomial of K.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0464216-9
PII: S 0002-9939(1978)0464216-9
Article copyright: © Copyright 1978 American Mathematical Society