Alexander modules of links with all linking numbers zero
HTML articles powered by AMS MathViewer
- by M. L. Platt
- Trans. Amer. Math. Soc. 306 (1988), 597-605
- DOI: https://doi.org/10.1090/S0002-9947-1988-0933308-0
- PDF | Request permission
Abstract:
In this paper we characterize the Alexander modules of links resulting from a surgical modification on the trivial link of any number of components. Using the presentation matrix obtained, we derive some properties of the Alexander polynomials of such links.References
- J. H. Bailey, Alexander invariants of links, Ph. D. thesis, Univ. of British Columbia, 1977.
- R. H. Crowell, Corresponding group and module sequences, Nagoya Math. J. 19 (1961), 27–40. MR 140559
- R. H. Crowell, Torsion in link modules, J. Math. Mech. 14 (1965), 289–298. MR 0174606
- Jonathan A. Hillman, Alexander ideals of links, Lecture Notes in Mathematics, vol. 895, Springer-Verlag, Berlin-New York, 1981. MR 653808
- Mark E. Kidwell, On the Alexander polynomials of certain three-component links, Proc. Amer. Math. Soc. 71 (1978), no. 2, 351–354. MR 482737, DOI 10.1090/S0002-9939-1978-0482737-X
- J. Levine, A method for generating link polynomials, Amer. J. Math. 89 (1967), 69–84. MR 224082, DOI 10.2307/2373097 —, The presentation matrix of a link module, preprint.
- J. Levine, The module of a $2$-component link, Comment. Math. Helv. 57 (1982), no. 3, 377–399. MR 689070, DOI 10.1007/BF02565866
- Yasutaka Nakanishi, A surgical view of Alexander invariants of links, Math. Sem. Notes Kobe Univ. 8 (1980), no. 1, 199–218. MR 590181
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
- Lorenzo Traldi, Linking numbers and the elementary ideals of links, Trans. Amer. Math. Soc. 275 (1983), no. 1, 309–318. MR 678352, DOI 10.1090/S0002-9947-1983-0678352-1
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 306 (1988), 597-605
- MSC: Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9947-1988-0933308-0
- MathSciNet review: 933308