Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T16:51:24.944Z Has data issue: false hasContentIssue false
  • English
  • Français

ALL STRONGLY-CYCLIC BRANCHED COVERINGS OF (1,1)-KNOTS ARE DUNWOODY MANIFOLDS

Published online by Cambridge University Press:  01 October 2004

ALESSIA CATTABRIGA  and
MICHELE MULAZZANI
ALESSIA CATTABRIGA
Affiliation:
Department of Mathematics, University of Bologna, [email protected]
MICHELE MULAZZANI
Affiliation:
Department of Mathematics and CIRAM, University of Bologna, [email protected]
Get access

Abstract

It is shown that every strongly-cyclic branched covering of a (1,1)-knot is a Dunwoody manifold. This result, together with the converse statement previously obtained by Grasselli and Mulazzani, proves that the class of Dunwoody manifolds coincides with the class of strongly-cyclic branched coverings of (1,1)-knots. As a consequence, a parametrization of (1,1)-knots by 4-tuples of integers is obtained. Moreover, using a representation of (1,1)-knots by the mapping class group of the twice-punctured torus, an algorithm is provided which gives the parametrization of all torus knots in $\mathbf{S}^3$.

Keywords

57M1257N10 (primary)57M25 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 70 , Issue 2 , October 2004 , pp. 512 - 528
Copyright
The London Mathematical Society 2004

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.)

Footnotes

This work was performed under the auspices of the GNSAGA, INdAM, Italy and the University of Bologna funds for selected research topics.