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COMPANIONS OF THE UNKNOT AND WIDTH ADDITIVITY

RYAN BLAIR

University of California, Santa Barbara, Mathematics Department, CA 93106, USA

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and

MAGGY TOMOVA

The University of Iowa, Mathematics Department, Iowa City, IA 52240, USA

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https://doi.org/10.1142/S0218216511009352Cited by:4 (Source: Crossref)

Abstract

It has been conjectured that for knots K and K′ in S³, w(K # K′) = w(K) + w(K′) - 2. In [7], Scharlemann and Thompson proposed potential counterexamples to this conjecture. For every n, they proposed a family of knots for which they conjectured that where Bⁿ is a bridge number n knot. We show that for n > 2 none of the knots in produces such counterexamples.

Keywords:

AMSC: 57M25, 57M27

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