English

When does a satellite knot fiber?

Geometric Topology 2007-05-23 v1

Abstract

Necessary and sufficient conditions are given for a satellite knot to be fibered. Any knot k~\tilde k embeds in an unknotted solid torus V~\tilde V with arbitrary winding number in such a way that no satellite knot with pattern (V~,k~)(\tilde V, \tilde k) is fibered. In particular, there exist nonfibered satellite knots with fibered pattern and companion knots and nonzero winding number.

Cite

@article{arxiv.0705.0012,
  title  = {When does a satellite knot fiber?},
  author = {Mikami Hirasawa and Kunio Murasugi and Daniel S. Silver},
  journal= {arXiv preprint arXiv:0705.0012},
  year   = {2007}
}
R2 v1 2026-06-21T08:23:38.756Z