THE SCHEME OF CHARACTERS IN SL2

Abstract

The aim of this article is to study the SL2(C)–character scheme of a finitely generated group. Given a presentation of a finitely generated group Γ, we give equations defining the coordinate ring of the scheme of SL2(C)–characters of Γ (finitely many equations when Γ is finitely presented). We also study the scheme of abelian and non-simple representations and characters. Finally we apply our results to study the SL2(C)–character scheme of the Borromean rings. ©2023 American Mathematical Society.