I am looking for orientable closed 3-manifolds in which there are no fibered knots. Although I know little about this, I think for links the answer to the question above is "no", and the result is usually formulated as the existence of open book decompositions. Can this result be upgraded to knots? If not, I would be interested in looking at examples, in which it is proved, that they contain no fibered knots. Preferably, I would like these spaces to be homology spheres, even better if Seifert fibered.
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The answer for knots is still "no", because if you have an open book decomposition with disconnected binding then you can stabilize it (see section 2 of Etnyre's lecture notes) by attaching a handle to the page with feet on different binding components. This reduces the number of binding components by one, and you can repeat until the binding is connected, in which case it is a fibered knot.
answered Jan 12, 2015 at 15:38