Knot adjacency and fibering |
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Authors: | Efstratia Kalfagianni Xiao-Song Lin |
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Institution: | Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 ; Department of Mathematics, University of California, Riverside, California 92521 |
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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 , examples of irreducible 3-manifolds that cannot be distinguished by the Cochran-Melvin finite type invariants of order . |
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Keywords: | Alexander polynomial knot adjacency fibered knots and 3-manifolds finite type invariants symplectic structures |
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