When does a satellite knot fiber?

Abstract

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.