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Geometric indices
and the Alexander polynomial of a knot


Author: Hirozumi Fujii
Journal: Proc. Amer. Math. Soc. 124 (1996), 2923-2933
MSC (1991): Primary 57M25
DOI: https://doi.org/10.1090/S0002-9939-96-03489-2
MathSciNet review: 1343693
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Abstract: It is well-known that any Laurent polynomial $\Delta (t)$ satisfying $\Delta (t)\allowbreak \doteq \Delta (t^{-1})$ and $\Delta (1) = \pm 1$ is the Alexander polynomial of a knot in $S^3$. We show that $\Delta (t)$ can be realized by a knot which has the following properties simultaneously: (i) tunnel number 1; (ii) bridge index 3; and (iii) unknotting number 1.


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Additional Information

Hirozumi Fujii
Affiliation: Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi, Osaka, Japan

DOI: https://doi.org/10.1090/S0002-9939-96-03489-2
Keywords: Tunnel number, bridge index, Alexander polynomial
Received by editor(s): March 15, 1995
Communicated by: Ronald Stern
Article copyright: © Copyright 1996 American Mathematical Society

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