A lower bound on the width of satellite knots

Alexander Zupan

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arXiv · 1008.2047

A lower bound on the width of satellite knots

Alexander Zupan

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Abstract

Thin position for knots in the 3-sphere was introduced by Gabai and has been used in a variety of contexts. We conjecture an analogue to a theorem of Schubert and Schultens concerning the bridge number of satellite knots. For a satellite knot K, we use the companion torus T to provide a lower bound for w(K), proving the conjecture for K with a 2-bridge companion. As a corollary, we find thin position for any satellite knot with a braid pattern and 2-bridge companion.

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Alexander Zupan. 2010-08-12. A lower bound on the width of satellite knots. https://arxiv.org/abs/1008.2047

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