Главная

Piotr Przytycki

  1. Bipolar Coxeter groups.

    Втр, 02/23/2010 - 16:01 — SomNambul
    Authors: Pierre-Emmanuel Caprace, Piotr Przytycki
    Subjects: Group Theory
    Abstract

    We consider the class of those Coxeter groups for which removing from the
    Cayley graph any tubular neighbourhood of any wall leaves exactly two connected
    components. We call these Coxeter groups bipolar. They include both the
    virtually Poincare duality Coxeter groups and the infinite irreducible
    2-spherical ones. We show in a geometric way that a bipolar Coxeter group
    admits a unique conjugacy class of Coxeter generating sets. Moreover, we
    provide a characterisation of bipolar Coxeter groups in terms of the associated
    Coxeter diagram.

  2. Twist-rigid Coxeter groups.

    Втр, 11/03/2009 - 16:01 — SomNambul
    Authors: Pierre-Emmanuel Caprace, Piotr Przytycki
    Subjects: Group Theory
    Abstract

    We prove that two angle-compatible Coxeter generating sets of a given
    finitely generated Coxeter group are conjugate provided one of them does not
    admit any elementary twist. This confirms a basic case of a general conjecture
    which describes a potential solution to the isomorphism problem for Coxeter
    groups.

  3. Acute triangulations of polyhedra and R^n.

    Втр, 09/22/2009 - 14:09 — SomNambul
    Authors: Eryk Kopczyński, Igor Pak, Piotr Przytycki
    Subjects: Metric Geometry
    Abstract

    We study the problem of acute triangulations of convex polyhedra and the
    space R^n. Here an acute triangulation is a triangulation into simplices whose
    dihedral angles are acute. We prove that acute triangulations of the n-cube do
    not exist for n>=4. Further, we prove that acute triangulations of the space
    R^n do not exist for n>= 5. In the opposite direction, in R^3, we present a
    construction of an acute triangulation of the cube, the regular octahedron and
    a non-trivial acute triangulation of the regular tetrahedron.

  4. Acute triangulations of polyhedra and R^n.

    Втр, 09/22/2009 - 14:09 — SomNambul
    Authors: Eryk Kopczyński, Igor Pak, Piotr Przytycki
    Subjects: Metric Geometry
    Abstract

    We study the problem of acute triangulations of convex polyhedra and the
    space R^n. Here an acute triangulation is a triangulation into simplices whose
    dihedral angles are acute. We prove that acute triangulations of the n-cube do
    not exist for n>=4. Further, we prove that acute triangulations of the space
    R^n do not exist for n>= 5. In the opposite direction, in R^3, we present a
    construction of an acute triangulation of the cube, the regular octahedron and
    a non-trivial acute triangulation of the regular tetrahedron.

Math-arch

RSS-материал