González Prieto, José ÁngelLogares Jiménez, Marina LucíaMartínez, JavierMuñoz, Vicente2023-06-222023-06-222023-03-10https://hdl.handle.net/20.500.14352/73104We describe the geometry of the character variety of representations of the fundamental group of the complement of a Hopf link with n twists, namely Γn=⟨x,y|[xn,y]=1⟩ into the group SU(r). For arbitrary rank, we provide geometric descriptions of the loci of irreducible and totally reducible representations. In the case r=2, we provide a complete geometric description of the character variety, proving that this SU(2)-character variety is a deformation retract of the larger SL(2,C)-character variety, as conjectured by Florentino and Lawton. In the case r=3, we also describe different strata of the SU(3)-character variety according to the semi-simple type of the representation.engjournal articleopen access512.7Character varietyRepresentation varietiesUnitary groupKnotsLinksGeometria algebraicaGrupos (Matemáticas)1201.01 Geometría Algebraica