The number of knot group representations is not a Vassiliev invariant
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- by Michael Eisermann PDF
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Abstract:
For a finite group $G$ and a knot $K$ in the $3$-sphere, let $F_G(K)$ be the number of representations of the knot group into $G$. In answer to a question of D. Altschuler we show that $F_G$ is either constant or not of finite type. Moreover, $F_G$ is constant if and only if $G$ is nilpotent. We prove the following, more general boundedness theorem: If a knot invariant $F$ is bounded by some function of the braid index, the genus, or the unknotting number, then $F$ is either constant or not of finite type.References
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Additional Information
- Michael Eisermann
- Affiliation: Mathematisches Institut der Universität Bonn, Beringstr. 1, 53115 Bonn, Germany
- Email: eiserm@math.uni-bonn.de
- Received by editor(s): July 9, 1998
- Published electronically: October 5, 1999
- Communicated by: Ronald A. Fintushel
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1555-1561
- MSC (1991): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-99-05287-9
- MathSciNet review: 1657727