When does a satellite knot fiber?

Details When does a satellite knot fiber? When does a satellite knot fiber?

2007-04-30

arxiv.org/abs/0705.0012v1

Mathematics

Geometric Topology

11 pages, 8 figures

Scientific paper

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

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