Publication: Stratification of SU(r)-character varieties of twisted Hopf links
Loading...
Official URL
Full text at PDC
Publication Date
2023-03-10
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Citations
Exportar
Abstract
We 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.
Description
UCM subjects
Unesco subjects
Keywords
Citation
[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).