Hostname: page-component-6bb9c88b65-g7ldn Total loading time: 0 Render date: 2025-07-25T17:42:39.115Z Has data issue: false hasContentIssue false
  • English
  • Français

Homotopy of Knots and the Alexander Polynomial

Published online by Cambridge University Press:  20 November 2018

David Austin  and
Dale Rolfsen
David Austin
Affiliation:
Department of Mathematics University of British Columbia Vancouver, British Columbia V6T 1Z2, email: daustin@math.ubc.ca
Dale Rolfsen
Affiliation:
Department of Mathematics University of British Columbia Vancouver, British Columbia V6T 1Z2, email: rolfsen@math.ubc.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Any knot in a 3-dimensional homology sphere is homotopic to a knot with trivial Alexander polynomial.

Keywords

57N1057M0557M2557N65

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 3 , 01 September 1999 , pp. 257 - 262
Copyright
Copyright © Canadian Mathematical Society 1999

References

[A] Austin, D., SU(2)-representations and the twisted signature of knots. In preparation.Google Scholar
[F] Freedman, M., The topology of four-dimensional manifolds. J. Differential Geom. 17 (1982), 357–454.Google Scholar
[FQ] Freedman, M. and Quinn, F., The Topology of 4-manifolds. Princeton University Press, 1990.Google Scholar
[Ka] Kauffman, L., Formal Knot Theory. Math. Notes 30, Princeton University Press, 1983.Google Scholar
[K] Kervaire, M., Les noeuds de dimensions supérieures. Bull. Soc. Math. France 93 (1965), 225–271.Google Scholar
[M] Milnor, J. W., Infinite cyclic coverings. Topology of Manifolds (Michigan State University, 1967), Prindle Weber Schmidt, Boston, 1968.Google Scholar
[R] Rolfsen, D., Knots and Links. Mathematics Lecture Series 7. Publish or Perish, 1976.Google Scholar
[S] Seifert, H., Über das Geschlect von Knoten. Math. Ann. 110 (1934), 571–592.Google Scholar