Stratification of SU(r)-character varieties of twisted Hopf links



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González-Prieto, Ángel and Logares Jiménez, Marina Lucía and Martínez, Javier and Muñoz, Vicente (2023) Stratification of SU(r)-character varieties of twisted Hopf links. (Unpublished)

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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.

Item Type:Article
Uncontrolled Keywords:Character variety; Representation varieties; Unitary group; Knots; Links
Subjects:Sciences > Mathematics > Algebraic geometry
Sciences > Mathematics > Group Theory
ID Code:77092
Deposited On:24 Mar 2023 15:12
Last Modified:24 Mar 2023 15:12

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