Small Seifert-fibered Dehn surgery on hyperbolic knots

John C. Dean

doi:10.2140/agt.2003.3.435

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arXiv · math/0306232

Small Seifert-fibered Dehn surgery on hyperbolic knots

John C. Dean

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Abstract

In this paper, we define the primitive/Seifert-fibered property for a knot in S^3. If satisfied, the property ensures that the knot has a Dehn surgery that yields a small Seifert-fibered space (i.e. base S^2 and three or fewer critical fibers). Next we describe the twisted torus knots, which provide an abundance of examples of primitive/Seifert-fibered knots. By analyzing the twisted torus knots, we prove that nearly all possible triples of multiplicities of the critical fibers arise via Dehn surgery on primitive/Seifert-fibered knots.

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BibTeX RIS

John C. Dean. 2003-06-15. Small Seifert-fibered Dehn surgery on hyperbolic knots. https://doi.org/10.2140/agt.2003.3.435

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