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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On composite twisted unknots


Author: Chaim Goodman-Strauss
Journal: Trans. Amer. Math. Soc. 349 (1997), 4429-4463
MSC (1991): Primary 57M25
MathSciNet review: 1355072
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Abstract: Following Mathieu, Motegi and others, we consider the class of possible composite twisted unknots as well as pairs of composite knots related by twisting. At most one composite knot can arise from a particular $V$-twisting of an unknot; moreover a twisting of the unknot cannot be composite if we have applied more than a single full twist. A pair of composite knots can be related through at most one full twist for a particular $V$-twisting, or one summand was unaffected by the twist, or the knots were the right and left handed granny knots. Finally a conjectured characterization of all composite twisted unknots that do arise is given.


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Additional Information

Chaim Goodman-Strauss
Affiliation: Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701
Email: strauss@math.utexas.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01627-9
PII: S 0002-9947(97)01627-9
Received by editor(s): August 8, 1994
Received by editor(s) in revised form: September 28, 1995
Article copyright: © Copyright 1997 American Mathematical Society