English

Exceptional surgeries on $(-2,p,p)$-pretzel knots

Geometric Topology 2011-02-08 v1

Abstract

We give a complete description of exceptional surgeries on pretzel knots of type (2,p,p)(-2, p, p) with p5p \ge 5. It is known that such a knot admits a unique toroidal surgery yielding a toroidal manifold with a unique incompressible torus. By cutting along the torus, we obtain two connected components, one of which is a twisted II-bundle over the Klein bottle. We show that the other is homeomorphic to the one obtained by certain Dehn filling on the magic manifold. On the other hand, we show that all such pretzel knots admit no Seifert fibered surgeries.

Keywords

Cite

@article{arxiv.1102.1118,
  title  = {Exceptional surgeries on $(-2,p,p)$-pretzel knots},
  author = {Kazuhiro Ichihara and In Dae Jong and Yuichi Kabaya},
  journal= {arXiv preprint arXiv:1102.1118},
  year   = {2011}
}

Comments

13 pages, 15 figures

R2 v1 2026-06-21T17:22:13.492Z