English

Seifert fibered surgeries with distinct primitive/Seifert positions

Geometric Topology 2011-10-18 v1

Abstract

We call a pair (K, m) of a knot K in the 3-sphere S^3 and an integer m a Seifert fibered surgery if m-surgery on K yields a Seifert fiber space. For most known Seifert fibered surgeries (K, m), K can be embedded in a genus 2 Heegaard surface of S^3 in a primitive/Seifert position, the concept introduced by Dean as a natural extension of primitive/primitive position defined by Berge. Recently Guntel has given an infinite family of Seifert fibered surgeries each of which has distinct primitive/Seifert positions. In this paper we give yet other infinite families of Seifert fibered surgeries with distinct primitive/Seifert positions from a different point of view. In particular, we can choose such Seifert surgeries (K, m) so that K is a hyperbolic knot whose complement S^3 - K has an arbitrarily large volume.

Keywords

Cite

@article{arxiv.1110.3609,
  title  = {Seifert fibered surgeries with distinct primitive/Seifert positions},
  author = {Mario Eudave-Munoz and Katura Miyazaki and Kimihiko Motegi},
  journal= {arXiv preprint arXiv:1110.3609},
  year   = {2011}
}

Comments

13 pages, 12 figures