Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Knot modules. I

Author: Jerome Levine
Journal: Trans. Amer. Math. Soc. 229 (1977), 1-50
MSC: Primary 57C45
MathSciNet review: 0461518
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Abstract: For a differentiable knot, i.e. an imbedding $ {S^n} \subset {S^{n + 2}}$, one can associate a sequence of modules $ \{ {A_q}\} $ over the ring $ Z[t,{t^{ - 1}}]$, which are the source of many classical knot invariants. If X is the complement of the knot, and $ \tilde X \to X$ the canonical infinite cyclic covering, then $ {A_q} = {H_q}(\tilde X)$. In this work a complete algebraic characterization of these modules is given, except for the Z-torsion submodule of $ {A_1}$.

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Article copyright: © Copyright 1977 American Mathematical Society