The universal character ring of some families of one-relator groups

We study the universal character ring of some families of one-relator groups. As an application, we calculate the universal character ring of two-generator one-relator groups whose relators are palindromic and, in particular, of the $(- 2, 2 m + 1, 2 n + 1)$ -pretzel knot for all integers $m$ and $n$ . For the $(- 2, 3, 2 n + 1)$ -pretzel knot, we give a simple proof of a result in [Trans. AMS, to appear] on its universal character ring, and an elementary proof of a result in [J. Knot Theory Ramif. 11 (2002) 1251–1289] on the number of irreducible components of its character variety.

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Keywords

character variety, universal character ring, pretzel knot, two-generator one-relator group, palindrome, tunnel number one knot

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 57N10

References

Publication

Received: 30 August 2012

Revised: 17 February 2013

Accepted: 2 April 2013

Published: 30 June 2013

Authors

Anh T Tran
Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, OH 43210 USA

Volume 13, issue 4 (2013)

Anh T Tran

Abstract