Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The number of knot group representations is not a Vassiliev invariant
HTML articles powered by AMS MathViewer

by Michael Eisermann PDF
Proc. Amer. Math. Soc. 128 (2000), 1555-1561 Request permission

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57M25
  • Retrieve articles in all journals with MSC (1991): 57M25
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