Arc distance equals level number

Sangbum Cho; Darryl McCullough; Arim Seo

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arXiv · 0901.1467

Arc distance equals level number

Sangbum Cho·Darryl McCullough·Arim Seo

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Abstract

A knot K in 1-bridge position with respect to a genus-g Heegaard surface in a 3-manifold can be moved by isotopy through knots in 1-bridge position until it lies in a union of n parallel genus-g surfaces tubed together by n-1 straight tubes, with K intersecting each tube in two arcs connecting the ends. We prove that the minimum n for which this is possible is equal to a Hempel-type distance invariant defined using an arc complex of the two holed genus-g surface

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Sangbum Cho, Darryl McCullough, Arim Seo. 2009-01-11. Arc distance equals level number. https://arxiv.org/abs/0901.1467

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