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WEIGHT ELEMENTS OF THE KNOT GROUPS OF SOME THREE-STRAND PRETZEL KNOTS
Published online by Cambridge University Press: 01 August 2018
Abstract
A knot group has weight one, so is normally generated by a single element called a weight element of the knot group. A meridian is a typical weight element, but some knot groups admit other weight elements. We show that for some infinite classes of three-strand pretzel knots and all prime knots with up to eight crossings, the knot groups admit weight elements that are not automorphic images of meridians.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 305 - 318
- Copyright
- © 2018 Australian Mathematical Publishing Association Inc.
Footnotes
The author was supported by JSPS KAKENHI grant no. JP16K05149.