Knot modules. I

Levine, Jerome

doi:10.1090/S0002-9947-1977-0461518-0

Knot modules. I
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Trans. Amer. Math. Soc. 229 (1977), 1-50 Request permission

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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