Knot adjacency and fibering

Kalfagianni, Efstratia; Lin, Xiao-Song

doi:10.1090/S0002-9947-08-04358-4

Knot adjacency and fibering
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by Efstratia Kalfagianni and Xiao-Song Lin PDF

Trans. Amer. Math. Soc. 360 (2008), 3249-3261 Request permission

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 knot adjacency can be used to obtain obstructions to the fibering of knots and of 3-manifolds. As an application, given a fibered knot $K’$, we construct infinitely many non-fibered knots that share the same Alexander module with $K’$. Our construction also provides, for every $n\in N$, examples of irreducible 3-manifolds that cannot be distinguished by the Cochran-Melvin finite type invariants of order $\leq n$.

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