Knot adjacency and fibering

Kalfagianni, Efstratia; Lin, Xiao-Song

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

Knot adjacency and fibering

Authors: Efstratia Kalfagianni and Xiao-Song Lin
Journal: Trans. Amer. Math. Soc. 360 (2008), 3249-3261
MSC (2000): Primary 57M25, 57M27, 57M50
DOI: https://doi.org/10.1090/S0002-9947-08-04358-4
Published electronically: January 30, 2008
MathSciNet review: 2379795
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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 , we construct infinitely many non-fibered knots that share the same Alexander module with . 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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