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Seifert fibered surgeries which do not arise from primitive/Seifert-fibered constructions

Thomas W. Mattman·Katura Miyazaki·Kimihiko Motegi
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Abstract

We construct two infinite families of knots each of which admits a Seifert fibered surgery with none of these surgeries coming from Dean's primitive/Seifert-fibered construction. This disproves a conjecture that all Seifert fibered surgeries arise from Dean's primitive/Seifert-fibered construction. The (-3,3,5)-pretzel knot belongs to both of the infinite families.

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Thomas W. Mattman, Katura Miyazaki, Kimihiko Motegi. 2005-02-15. Seifert fibered surgeries which do not arise from primitive/Seifert-fibered constructions. https://arxiv.org/abs/math/0502303

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