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On composite twisted unknots

Author(s): Chaim Goodman-Strauss
Journal: Trans. Amer. Math. Soc. 349 (1997), 4429-4463.
MSC (1991): Primary 57M25
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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: 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
Copyright of article: Copyright 1997, American Mathematical Society

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