English

Small Seifert-fibered Dehn surgery on hyperbolic knots

Geometric Topology 2014-10-01 v1

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.

Keywords

Cite

@article{arxiv.math/0306232,
  title  = {Small Seifert-fibered Dehn surgery on hyperbolic knots},
  author = {John C. Dean},
  journal= {arXiv preprint arXiv:math/0306232},
  year   = {2014}
}

Comments

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-14.abs.html

R2 v1 2026-07-22T16:55:26.825Z