Free Seifert surfaces and disk decompositions

Mark Brittenham

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arXiv · math/9910066

Free Seifert surfaces and disk decompositions

Mark Brittenham

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Abstract

A Seifert surface F for a knot K is disk decomposable if there is a taut sutured manifold heirarchy for the complement of F, whose decomposing surfaces are all disks. It follows that F has minimal genus for the knot K, and has handlebody complement, i.e., F is free. We show that these necessary conditions for disk decomposability are not sufficient, by constructing a family of knots with genus one free Seifert surfaces, which are not disk decomposable.

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Mark Brittenham. 1999-10-13. Free Seifert surfaces and disk decompositions. https://arxiv.org/abs/math/9910066

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