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More interlinked loops

Published online by Cambridge University Press:  01 August 2016

W. R. Brakes  and
G. C. Shephard
W. R. Brakes
Affiliation:
The University of Northampton, Moulton Park, Northampton NN3 7AL email: billl40347@btinternet.com
G. C. Shephard
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ email: G.C.Shephard@uea.ac.uk
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Extract

In the second named author presented some results and problems concerning interlinked loops. These were ‘inspired’ by the well-known Borromean rings – three loops with the property that they are interlinked, but if we cut and remove any one of the loops, then the remaining two loops are not linked and so can be separated.

To conform more closely with standard terminology in this area we shall here use the term ‘link of n components’ to denote such a set of loops (rather than linkage). In all the cases we consider, the individual loops that make up each link are unknotted.

Type
Articles
Information
The Mathematical Gazette , Volume 93 , Issue 527 , July 2009 , pp. 222 - 227
Copyright
Copyright © The Mathematical Association 2009

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References

1. Shephard, G.C., Interlinked loops, Math. Gaz. 90 (July 2006) pp. 249–252.Google Scholar
2. Brunn, H., Ueber Verkettung, Sitzungsberichte der Bayerischen Akademie der Wissenschaften, Mathematosch-Physikalische Klasse, 22 (1892) pp. 77–99.Google Scholar
3. DeBrunner, H., Links of Brunnian type, Duke Math. J., 28 (1961) pp. 17–23.Google Scholar
4. Penney, D.E., Generalized Brunnian links, Duke Math. J., 36 (1969) pp. 31–32.Google Scholar
5. Lickorish, W.B. Raymond, An introduction to knot theory (Graduate Texts in Mathematics), Springer-Verlag New York Inc. (1997).Google Scholar