Character varieties of \((-2,2m+1,2n)\)-pretzel links and twisted Whitehead links (Q2796947)

Let \(\Gamma\) be a finitely generated group, \(G\) a complex reductive affine algebraic group, and \(\mathfrak X(\Gamma, G)\) the GIT quotient of \(\mathrm{Hom}(\Gamma, G)\) by the conjugation action of \(G\). The affine algebraic set \(\mathfrak{X}(\Gamma, G)\) is called the \textit{\(G\)-character variety of \(\Gamma\)}.NEWLINENEWLINEIn this paper, when \(G=\mathrm{SL}(2,\mathbb C)\) and \(\Gamma\) is the fundamental group of certain link complements in \(S^3\) the author describes the irreducible components of the corresponding character variety. In particular, the cases of pretzel links, twisted Whitehead links, and two-bridge links are considered.