Hostname: page-component-6bf8c574d5-8gtf8 Total loading time: 0 Render date: 2025-02-14T10:44:04.518Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal presentations for solvable 2-knot groups

Published online by Cambridge University Press:  17 April 2009

Jonathan A. Hillman
Jonathan A. Hillman
Affiliation:
School of Mathematics and StatisticsThe University of SydneySydney NSW 2006Australia e-mail: [email protected]
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.

We find presentations for the groups of Cappell-Shaneson 2-knots and other solvable 2-knot groups which are optimal in terms of deficiency and number of generators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 129 - 133
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Aitchison, I.R. and Rubinstein, J.H., ‘Fibered knots and involutions on homotopy spheres’, in Four-manifold theory, (Gordon, C. McA. and Kirby, R.C., Editor) (American Mathematical Society, Providence R.I., 1984), pp. 1–74.Google Scholar
[2]Cappell, S.E. and Shaneson, J.L., ‘There exist inequivalent knots with the same complement’, Ann. of Math. 103 (1976), 349–353.CrossRefGoogle Scholar
[3]Hillman, J.A., Alexander ideals of links, Lecture Notes in Mathematics 895 (Springer-Verlag, Berlin, Heidelberg, New York, 1981).CrossRefGoogle Scholar
[4]Hillman, J.A., Two-knots and their groups, Australian Mathematical Society Lecture Series 9 (Cambridge University Press, 1989).Google Scholar
[5]Hillman, J.A., ‘Tits alternatives and low dimensional topology’, (preprint, The University of Sydney, 1997).Google Scholar
[6]Yoshikawa, K., ‘On 2-knot groups with the finite commutator subgroup’, Math. Sem. Notes Kobe Univ. 8 (1980), 321–330.Google Scholar