The scheme of characters in SL 2
Abstract
The aim of this article is to study the SL(2,C)-character scheme of a finitely generated group. Given a presentation of a finitely generated group , we give equations defining the coordinate ring of the scheme of SL(2,C)-characters of (finitely many equations when is finitely presented). We also study the scheme of abelian and nonsimple representations and characters. Finally we apply our results to study the SL(2,C)-character scheme of the Borromean rings.
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