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

Published electronically:
January 30, 2008

MathSciNet review:
2379795

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Abstract | References | Similar Articles | Additional Information

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 , examples of irreducible 3-manifolds that cannot be distinguished by the Cochran-Melvin finite type invariants of order .

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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:
https://doi.org/10.1090/S0002-9947-08-04358-4

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

Published electronically:
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

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.