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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The universal character ring of some families of one-relator groups

Anh T Tran

Algebraic & Geometric Topology 13 (2013) 2317–2333
Abstract

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 (2,2m + 1,2n + 1)-pretzel knot for all integers m and n. For the (2,3,2n + 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.

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