Talk:Character variety

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Variants
It is not clear if the variant attributed here to Culler-Shalen, is different to the idea of "rings of Fricke characters" (in the title of the paper of Magnus) that presumably goes back to Fricke. Both the work of Fricke (and Vogt) and the Annals paper of Culler-Shalen focus on SL_2 where the two possible definitions give the same variety. Should we not just abandon this other possible definition? Does any one seriously use it in any case where it gives a genuinely different variety? Alternatively can we change the section "Variants" to say that for SL_2 there is an alternative definition (used by Fricke, Culler-Shalen) that gives the same variety? — Preceding unsigned comment added by Ccgim (talk • contribs) 11:29, 8 April 2022 (UTC)