Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2025-01-01T16:05:52.838Z Has data issue: false hasContentIssue false
  • English
  • Français

The Torres conditions are insufficient

Published online by Cambridge University Press:  24 October 2008

Jonathan A. Hillman
Jonathan A. Hillman
Affiliation:
University of Durham
Get access Rights & Permissions [Opens in a new window]

Extract

In this note we shall show that the conditions given by G. Torres in (7) do not suffice to characterize the first Alexander polynomial of a link. We shall recall below Torres' results (for the 2-component case) and state the result of J. H. Bailey on which our argument relies, and then prove the following theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 19 - 22
Copyright
Copyright © Cambridge Philosophical Society 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

(1)Bailey, J. H. Alexander Invariants of Links. Ph.D. thesis, University of British Columbia, 1977.Google Scholar
(1 bis)Bailey, J. H.A characterization of Alexander invariants of links. Abstract 77T-G69. Notices A.M.S. 24 (1977), A–396.Google Scholar
(2)KidWell, M. E.Alexander polynomials of links of small order. Illinois J. Math. 22 (1978), 459–475.CrossRefGoogle Scholar
(3)Levine, J. P.A method for generating link polynomials. Amer. J. Math. 89 (1967), 69–84.CrossRefGoogle Scholar
(4)Masley, J.On Euclidean rings of integers in cyclotomic fields. J. reine angew. Math. 272 (1975), 45–48.Google Scholar
(5)Sato, N. A. Alexander modules of sublinks and an invariant of link concordance. Preprint.Google Scholar
(6)Serre, J.-P.Corps Locaux Hermann, Paris, 1968.Google Scholar
(7)Torres, G.On the Alexander polynomial. Ann. Math. 57 (1953), 57–89.CrossRefGoogle Scholar