Browsing by Author "Vaskou, Nicolas"

Filter results by typing the first few letters
Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Algebraic and geometric aspects of two-dimensional Artin groups
    (Heriot-Watt University, 2023-04) Vaskou, Nicolas; Martin, Alexandre
    In this thesis we study the algebra and the geometry of two-dimensional Artin groups under various aspects. First, we solve the problem of acylindrical hyperbolicity, by proving that all the two-dimensional Artin groups that are not trivially non-acylindrically-hyperbolic are acylindrically hyperbolic. In particular, we prove that every non-spherical Artin group of dimension 2 has trivial centre. Then, we study the structure of parabolic subgroups of large-type Artin groups, and prove various results about their combinatorial structure. We notably show that any intersection of parabolic subgroups is again a parabolic subgroup. Finally, we study the isomorphisms between Artin groups of large-type, and we prove that the family of large-type free-of-infnity Artin groups is rigid. We also fully describe the automorphism groups of these Artin groups.