Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 
 

 

Alexander modules of links with all linking numbers zero


Author: M. L. Platt
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [B] J. H. Bailey, Alexander invariants of links, Ph. D. thesis, Univ. of British Columbia, 1977.
  • [C] R. H. Crowell, Corresponding group and module sequences, Nagoya Math. J. 19 (1961), 27-40. MR 0140559 (25:3977)
  • [C-1] -, Torsion in link modules, J. Math. Mech. 14 (1965), 289-298. MR 0174606 (30:4807)
  • [H] J. A. Hillman, Alexander ideals of links, Lecture Notes in Math., vol. 895, Springer-Verlag, New York, 1981. MR 653808 (84j:57004)
  • [K] M. Kidwell, On the Alexander polynomial of certain three component links, Proc. Amer. Math. Soc. 71 (1978), 351-353. MR 0482737 (58:2791)
  • [L] J. P. Levine, A method for generating link polynomials, Amer. J. Math. 89 (1967), 69-84. MR 0224082 (36:7129)
  • [L-1] -, The presentation matrix of a link module, preprint.
  • [L-2] -, The module of a two-component link, Comment. Math. Helv. 57 (1982), 377-399. MR 689070 (84h:57003)
  • [N] Y. Nakaniski, A surgical view of Alexander invariants of links, Math. Sem. Notes Kobe Univ. 8 (1980), 199-218. MR 590181 (82j:57004)
  • [R] D. Rolfsen, Knots and links, Publish or Perish, Berkeley, Calif., 1976. MR 0515288 (58:24236)
  • [T] L. Tradi, Linking numbers and elementary ideals of links, Trans. Amer. Math. Soc. 275 (1983). MR 678352 (84d:57002)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57M25

Retrieve articles in all journals with MSC: 57M25


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-0933308-0
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society