Antolín Pichel, Yago

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First Name
Last Name
Antolín Pichel
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Álgebra, Geometría y Topología
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Now showing 1 - 8 of 8
  • Publication
    Subgroups of even Artin groups of FC-type
    (2023-05-26) Antolín Pichel, Yago; Foniqi, Islam
    We prove a Tits alternative theorem for subgroups of finitely generated even Artin groups of FC type (EAFC groups), stating that there exists a finite index subgroup such that every subgroup of it is either finitely generated abelian, or maps onto a non-abelian free group. Parabolic subgroups play a key role, and we show that parabolic subgroups of EAFC groups are closed under taking roots.
  • Publication
    Geodesic Growth of some 3-dimensional RACGs
    (2021) Antolín Pichel, Yago; Foniqi, Islam
    We give explicit formulas for the geodesic growth series of a Right Angled Coxeter Group (RACG) based on a link-regular graph that is 4-clique free, i.e. without tetrahedrons.
  • Publication
    Intersection of parabolic subgroups in even Artin groups of FC-type
    (Cambridge University Press, 2022-10-18) Antolín Pichel, Yago; Foniqi, Islam
    We show that the intersection of parabolic subgroups of an even finitely generated FC-type Artin group is again a parabolic subgroup.
  • Publication
    Parabolic subgroups acting on the additional length graph
    (Mathematical Sciences Publishers (MSP), 2021) Antolín Pichel, Yago; Cumplido, María
    Let A ≠ A1;A2;I2m be an irreducible Artin–Tits group of spherical type. We show that the periodic elements of A and the elements preserving some parabolic subgroup of A act elliptically on the additional length graph CAL(A), a hyperbolic, infinite diameter graph associated to A constructed by Calvez and Wiest to show that A/Z(A) is acylindrically hyperbolic. We use these results to find an element g ∈ A such that ≅ P * for every proper standard parabolic subgroup P of A. The length of g is uniformly bounded with respect to the Garside generators, independently of A. This allows us to show that, in contrast with the Artin generators case, the sequence ω(An,S)(with n ∈ N) of exponential growth rates of braid groups, with respect to the Garside generating set, goes to infinity.
  • Publication
    Bredon homology of artin groups of dihedral type
    (2022) Antolín Pichel, Yago; Flores, Ramón
    For Artin groups of dihedral type, we compute the Bredon homology groups of theclassifying space for the family of virtually cyclic subgroups with coefficients in the K-theory of a group ring.
  • Publication
    Regular left-orders on groups
    (2021-04-12) Antolín Pichel, Yago; Rivas, Cristóbal; Lu Su, Hang
    A regular left-order on finitely generated group a group G is a total, left-multiplication invariant order on G whose corresponding positive cone is the image of a regular language over the generating set of the group under the evaluation map. We show that admitting regular left-orders is stable under extensions and wreath products and give a classification of the groups all whose left-orders are regular left-orders. In addition, we prove that solvable Baumslag-Solitar groups B(1, n) admits a regular left-order if and only if n ≥ −1. Finally, Hermiller and Sunic showed that no free product admits a regular left-order, however we show that if A and B are groups with regular left-orders, then (A ∗ B) × Z admits a regular left-order.
  • Publication
    On the asymptotics of visible elements and homogeneous equations in surface groups
    (EMS Press, 2012) Antolín Pichel, Yago; Ciobanu, Laura; Viles, Noelia
    Let F be a group whose abelianization is Zk, k 2. An element of F is called visible if its image in the abelianization is visible, that is, the greatest common divisor of its coordinates is 1. In this paper we compute three types of densities, annular, even and odd spherical, of visible elements in surface groups. We then use our results to show that the probability of a homogeneous equation in a surface group to have solutions is neither 0 nor 1, as the lengths of the right- and left-hand side of the equation go to infinity.
  • Publication
    The Hanna Neumann conjecture for surface groups
    (Cambridge University Press, 2022-10-12) Antolín Pichel, Yago; Jaikin-Zapirain, Andrei
    The Hanna Neumann conjecture is a statement about the rank of the intersection of two finitely generated subgroups of a free group. The conjecture was posed by Hanna Neumann in 1957. In 2011, a strengthened version of the conjecture was proved independently by Joel Friedman and by Igor Mineyev. In this paper we show that the strengthened Hanna Neumann conjecture holds not only in free groups but also in non-solvable surface groups. In addition, we show that a retract in a free group and in a surface group is inert. This implies the Dicks–Ventura inertia conjecture for free and surface groups.