Seifert fibered surgeries with distinct primitive/Seifert positions
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