González-Prieto, ÁngelLogares Jiménez, Marina LucíaMartínez, JavierMuñoz, Vicente2023-06-222023-06-222023-03-10[1] H.U. Boden, Representations of orbifold groups and parabolic bundles, Comment. Math. Helv. 66 (1991) 389-447. [2] G. Burde and K. Murasugi, Links and Seifert fiber spaces, Duke Math. J. 37 (1970) 89-93. [3] H. Chen and T. Yu, The SL(2;C)-character variety of the Borromean link, arXiv:2202.07429. [4] C. Florentino, P. Gothen and A. Nozad, Homotopy type of moduli spaces of G-Higgs bundles and reducibility of the nilpotent cone, Bull. Sci. Math. 150 (2019) 84-101. [5] C. Florentino and S. Lawton, Flawed groups and the topology of character varieties, arXiv:2012.08481. [6] M. Furuta and B. Steer, Seifert Fibred Homology 3-Spheres and the Yang-Mills equations on Riemann surfaces with marked points, Adv. Math. 96 (1992) 38-102. [7] Á. González-Prieto, J. Martínez and V. Muñoz, Geometry of SU(3)-character varieties of torus knots, Topology and its Applications. Special volume in honor to 70th birthday of J.M.R. Sanjurjo. To appear [8] Á. González-Prieto and V. Muñoz, Motive of the SL4-character variety of torus knots, Journal of Algebra 610 (2022) 852-895. [9] Á. González-Prieto and V. Muñoz, Representation varieties of twisted Hopf links, Mediterranean Journal of Mathematics, 2023, article 89. [10] J. Martínez and V. Muñoz, The SU(2)-character varieties of torus knots, Rocky Mountain J. Math. (2) 45 (2015) 583-600. [11] V.B. Mehta and C.S. Seshadri, Moduli of Vector Bundles on Curves with Parabolic Structures, Math. Ann. 248 (1980) 205-240. [12] V. Muñoz, The SL(2;C)-character varieties of torus knots, Rev. Mat. Complut. 22 (2009) 489-497. [13] B. Nasatyr and B. Steer, Orbifold Riemann surfaces and the Yang-Mills-Higgs equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 22 (1995) 595-643. [14] P.E. Newstead, Topological properties of some spaces of stable bundles, Topology 6 (1967) 241-262. [15] P.E. Newstead, Introduction to moduli problems and orbit spaces, TIFR Lect. Notes, 51 (1978).https://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