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The realization problem for noninteger Seifert fibered surgeries

Ahmad Issa and Duncan McCoy

Algebraic & Geometric Topology 23 (2023) 1501–1550

Conjecturally, the only knots in S3 with noninteger surgeries producing Seifert fibered spaces are torus knots and cables of torus knots. We make progress on the associated realization problem. Let Y be a small Seifert fibered space arising by pq–surgery on a knot in S3, where pq is positive and a noninteger. Let e denote the weight of the central vertex in the minimal star-shaped plumbing that Y bounds. We show that if e 2 or e 3, then Y can be obtained by pq–surgery on a torus knot or a cable of a torus knot.

Dehn surgery, Seifert fibered spaces, changemaker lattices, exceptional surgeries, Heegaard Floer homology
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Received: 22 October 2018
Revised: 14 June 2021
Accepted: 24 October 2021
Published: 14 June 2023
Ahmad Issa
Department of Mathematics
University of British Columbia
Vancouver, BC
Duncan McCoy
Département de mathématiques
Université du Québec à Montréal
Montreal, QC

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