Talk:Fibered knot

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This sounds like a knot is fibered if it is the binding of an open book decomposition of the 3-sphere. Is that right, or does the fibered condition require trivial monodromy? Orthografer 21:29, 18 September 2006 (UTC)[reply]

Answer: a knot is fibered if and only if it is the binding of some open book decomposition of ${\displaystyle S^{3}}$, with no monodromy restrictions. Orthografer 20:30, 8 September 2007 (UTC)[reply]

What is an example on a knot that isn't fibered? I think that should be mentioned in the article (as well as the answer above).--agr (talk) 13:49, 20 May 2008 (UTC)[reply]

It is known that the Alexander polynomial of a knot is monic if the knot is fibered. By monic, I mean that the coefficients of the highest and lowest powers of t are plus or minus 1. Examples of knots with nonmonic Alexander polynomials abound - the twist knots have Alexander polynomials qt−(2q+1)+qt⁻¹, where q is the number of half-twists. See this paper if you'd like a reference. Orthografer (talk) 23:55, 21 May 2008 (UTC)[reply]

The Introduction presents a definition of fibred knot that is completely inadequate, because it's easy to think of situations satisfying the definition that are most definitely not what "fibred knot" means.50.205.142.50 (talk) 17:46, 27 May 2020 (UTC)[reply]