Longitudes of a link and principality of an Alexander ideal
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- by Jonathan A. Hillman PDF
- Proc. Amer. Math. Soc. 72 (1978), 370-374 Request permission
Abstract:
In this note it is shown that the longitudes of a $\mu$-component homology boundary link L are in the second commutator subgroup G” of the link group G if and only if the $\mu$th Alexander ideal ${\mathcal {E}_\mu }(L)$ is principal, generalizing the result announced for $\mu = 2$ by R. H. Crowell and E. H. Brown. These two properties were separately hypothesized as characterizations of boundary links by R. H. Fox and N. F. Smythe.References
- R. H. Crowell, Corresponding group and module sequences, Nagoya Math. J. 19 (1961), 27–40. MR 140559 —, Private communication to N. F. Smythe, May 1976.
- M. A. Gutiérrez, Polynomial invariants of boundary links, Rev. Colombiana Mat. 8 (1974), 97–109. MR 0367969
- H. W. Lambert, A $1$-linked link whose longitudes lie in the second commutator subgroup, Trans. Amer. Math. Soc. 147 (1970), 261–269. MR 267568, DOI 10.1090/S0002-9947-1970-0267568-5
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288 N. F. Smythe, Boundary links, Topology Seminar, Wisconsin, 1965, Ann. of Math. Studies, No. 60, Princeton Univ. Press, Princeton, N. J., 1966, pp. 69-72.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 370-374
- MSC: Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-1978-0507341-6
- MathSciNet review: 507341