Logares Jiménez, Marina Lucía

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First Name
Marina Lucía
Last Name
Logares Jiménez
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Álgebra, Geometría y Topología
Geometría y Topología
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Now showing 1 - 2 of 2
  • Publication
    Stratification of SU(r)-character varieties of twisted Hopf links
    (2023-03-10) González-Prieto, Ángel; Logares Jiménez, Marina Lucía; Martínez, Javier; Muñoz, Vicente
    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.
  • Publication
    Representation Variety for the Rank One Affine Group
    (Springer, 2021) González Prieto, José Ángel; Logares Jiménez, Marina Lucía; Muñoz, Vicente
    The aim of this chapter is to study the virtual classes of representation varieties of surface groups onto the rank one affine group. We perform this calculation by three different approaches: the geometric method, based on stratifying the representation variety into simpler pieces; the arithmetic method, focused on counting their number of points over finite fields; and the quantum method, which performs the computation by means of a Topological Quantum Field Theory. We also discuss the corresponding moduli spaces of representations and character varieties, which turn out to be non-equivalent due to the non-reductiveness of the underlying group.