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Knot adjacency and fibering

Author(s): Efstratia Kalfagianni; Xiao-Song Lin
Journal: Trans. Amer. Math. Soc. 360 (2008), 3249-3261.
MSC (2000): Primary 57M25, 57M27, 57M50
Posted: January 30, 2008
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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 $ 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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Additional Information:

Efstratia Kalfagianni
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: kalfagia@math.msu.edu

Xiao-Song Lin
Affiliation: Department of Mathematics, University of California, Riverside, California 92521

DOI: 10.1090/S0002-9947-08-04358-4
PII: S 0002-9947(08)04358-4
Keywords: Alexander polynomial, knot adjacency, fibered knots and 3-manifolds, finite type invariants, symplectic structures
Received by editor(s): July 15, 2005
Received by editor(s) in revised form: June 27, 2006
Posted: January 30, 2008
Additional Notes: The research of the authors was partially supported by the NSF
Xiao-Song Lin passed away on January 14, 2007
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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