Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 4
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Cochran, Tim 1984. Embedding 4-manifolds in S5. Topology, Vol. 23, Issue. 3, p. 257.
    Hillman, Jonathan A. 1981. A link with Alexander module free which is not an homology boundary link. Journal of Pure and Applied Algebra, Vol. 20, Issue. 1, p. 1.
    Hillman, Jonathan A. 1980. Trivializing ribbon links by Kirby moves. Bulletin of the Australian Mathematical Society, Vol. 21, Issue. 01, p. 21.
    Hillman, Jonathan Arthur 1979. Knots and links in low dimensions. Bulletin of the Australian Mathematical Society, Vol. 20, Issue. 01, p. 149.
    ×
  • Access

A non-homology boundary link with zero Alexander polynomial

  • Jonathan A. Hillman (a1)
Abstract

This paper presents a necessary condition for a ribbon link to be an homology boundary link and gives a consequent simple counterexample to the conjecture of Smythe that the vanishing of the first Alexander polynomial characterizes homology boundary links among all 2-component links.

    •
      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A non-homology boundary link with zero Alexander polynomial
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      A non-homology boundary link with zero Alexander polynomial
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      A non-homology boundary link with zero Alexander polynomial
      Available formats
      ×
Copyright
COPYRIGHT: © Australian Mathematical Society 1977
References
Hide All
[1]Atiyah, M.F., Macdonald, I.G., Introduction to commutative algebra (Addison-Wesley, Reading, Massachusetts; Menlo Park, California; London; Don Millas, Ontario; 1969).
[2]Bass, Hyman, “Libération des modules projectifs sur certains anneaux de polynômes”, Séminaire Bourbaki, 26e année, 1973/74, no. 448, 228–254 (Lecture Notes in Mathematics, 431. Springer-Verlag, Berlin, Heidelberg, New York, 1975).
[3]Baumslag, Gilbert, “Groups with the same lower central sequence as a relatively free group. I: The groups”, Trans. Amer. Math. Soc. 129 (1967), 308–321.
[4]Cochran, David S., “Links with zero Alexander polynomial” (PhD thesis, Dartmouth College, Hanover, New Hampshire, 1970).
[5]Crowell, R.H., “Corresponding group and module sequences”, Nagoya Math. J. 19 (1961), 27–40.
[6]Crowell, R.H., “Torsion in link modules”, J. Math. Mech. 14 (1965), 289–298.
[7]Fox, R.H., “Some problems in knot theory”, Topology of 3-manifolds and related tcpics, 168–176 (Proceedings of the University of Georgia Institute, 1961. Prentice-Hall, Englewood Cliffs, New Jersey, 1902).
[8]Hillman, Jonathan A., “Alexander ideals and Chen groups”, submitted.
[9]Kauffman, Louis H. and Taylor, Laurence R., “Signature of links”, Trans. Amer. Math. Soc. 216 (1976), 351–365.
[10]Murasugi, Kunio, “On a certain numerical invariant of link types”, Trans. Amer. Math. Soc. 117 (1965), 387–422.
[11]Neuwirth, L.P., Knot groups (Annals of Mathematics Studies, 56. Princeton University Press, Princeton, New Jersey, 1965).
[12]Quillen, Daniel, “Projective modules over polynomial rings”, Inventiones Math. 36 (1976), 167–171.
[13]Smythe, N., “Boundary links”, Topology seminar, Wisconsin, 1965, 69–72 (Annals of Mathematics Studies, 60. Princeton University Press, Princeton, New Jersey, 1966).
[14]Sumners, D.W., “Invertible knot cobordisms”, Topology of manifolds, 200–204 (Proceedings of the University of Georgia Topology of Manifolds Institute, 1969. Markham, Chicago, 1970).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 59 *
Loading metrics...

Abstract views

Total abstract views: 46 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×