Knot adjacency and fibering

Abstract

It is known that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of &#34;knot adjacency&#34;, studied in the paper &#34;Knot adjacency, genus and essential tori&#34; by the authors, can be used to obtain obstructions to fibering of knots and of 3-manifolds. As an application, given a fibered knot K&#39;, we construct infinitely many non-fibered knots that share the same Alexander module and the same Vassiliev invariants up to certain orders with K&#39;. Our construction also provides, for every natural number n, examples of irreducible 3-manifolds that cannot be distinguished by the Cochran-Melvin finite type invariants of order < n.