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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Knot modules. I
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by Jerome Levine
Trans. Amer. Math. Soc. 229 (1977), 1-50
DOI: https://doi.org/10.1090/S0002-9947-1977-0461518-0

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 ${A_1}$.
References
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Bibliographic Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 229 (1977), 1-50
  • MSC: Primary 57C45
  • DOI: https://doi.org/10.1090/S0002-9947-1977-0461518-0
  • MathSciNet review: 0461518