Person:
Muñoz Velázquez, Vicente

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First Name
Vicente
Last Name
Muñoz Velázquez
URI
https://hdl.handle.net/20.500.14352/84910
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Area
Geometría y Topología
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2020 - 20234
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Now showing 1 - 4 of 4
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    A lax monoidal Topological Quantum Field Theory for representation varieties
    (Bulletin des Sciences Mathématiques, 2020) González Prieto, José Ángel; Logares Jiménez, Marina Lucía; Muñoz Velázquez, Vicente
    We construct a lax monoidal Topological Quantum Field Theory that computes Deligne-Hodge polynomials of representation varieties of the fundamental group of any closed manifold into any complex algebraic group G. As byproduct, we obtain formulas for these polynomials in terms of homomorphisms between the space of mixed Hodge modules on G. The construction is developed in a categorical-theoretic framework allowing its application to other situations.
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    Representation Varieties of Twisted Hopf Links
    (Mediterranean Journal of Mathematics, 2023) González Prieto, José Ángel; Muñoz Velázquez, Vicente
    In this paper, we study the representation theory of the fundamental group of the complement of a Hopf link with n twists. A general framework is described to analyze the -representation varieties of these twisted Hopf links as byproduct of a combinatorial problem and equivariant Hodge theory. As application, close formulas of their E-polynomials are provided for ranks 2 and 3, both for the representation and character varieties.
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    Motive of the representation varietes of torus knots for low rank affine groups
    (2022) González Prieto, José Ángel; Logares Jiménez, Marina Lucía; Muñoz Velázquez, Vicente
    We compute the motive of the variety of representations of the torus knot of type (m, n) into the affine groups AGL1(C) and AGL2(C). For this, we stratify the varieties and show that the motives lie in the subring generated by the Lefschetz motive q = [C].
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    Representation Variety for the Rank One Affine Group
    (Mathematical Analysis in Interdisciplinary Research, 2021) González Prieto, José Ángel; Logares Jiménez, Marina Lucía; Muñoz Velázquez, 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.