Geodesic
The universal character ring of some families of one-relator groups
Tran, Anh T1
1Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USA
Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2317-2333
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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.

DOI : 10.2140/agt.2013.13.2317
Classification : 57M27, 57N10
Keywords: character variety, universal character ring, pretzel knot, two-generator one-relator group, palindrome, tunnel number one knot

Tran, Anh T  1

1 Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USA 
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Tran, Anh T. The universal character ring of some families of one-relator groups. Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2317-2333. doi: 10.2140/agt.2013.13.2317

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