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WEIGHT ELEMENTS OF THE KNOT GROUPS OF SOME THREE-STRAND PRETZEL KNOTS

Part of: Low-dimensional topology

Published online by Cambridge University Press:  01 August 2018

MASAKAZU TERAGAITO Open the ORCID record for MASAKAZU TERAGAITO [Opens in a new window]
MASAKAZU TERAGAITO*
Affiliation:
Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima, 739-8524, Japan email teragai@hiroshima-u.ac.jp
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Abstract

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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.

Keywords

weight elementknot grouppretzel knotbalanced presentation

MSC classification

Primary: 57M25: Knots and links in $S^3$
Secondary: 57M05: Fundamental group, presentations, free differential calculus
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.

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