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

Mattman, Thomas; Miyazaki, Katura; Motegi, Kimihiko

doi:10.1090/S0002-9947-05-03798-0

Seifert-fibered surgeries which do not arise from primitive/Seifert-fibered constructions
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by Thomas Mattman, Katura Miyazaki and Kimihiko Motegi PDF

Trans. Amer. Math. Soc. 358 (2006), 4045-4055 Request permission

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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