Calculating canonical distinguished involutions in the affine Weyl groups.
Character theory of symmetric groups, analysis of long relators, and random walks.
Chromatic Plane Compositions
Classical projective geometry and arithmetic groups.
Clifford k-algebras and k*-groups.
Clusters in middle-phase percolation on hyperbolic plane
I consider p-Bernoulli bond percolation on transitive, nonamenable, planar graphs with one end and on their duals. It is known from [BS01] that in such a graph G we have three essential phases of percolation, i.e. , where is the critical probability and -the unification probability. I prove that in the middle phase a.s. all the ends of all the infinite clusters have one-point boundaries in ∂ℍ². This result is similar to some results in [Lal].
Coarse structures and group actions
The main results of the paper are: Proposition 0.1. A group G acting coarsely on a coarse space (X,𝓒) induces a coarse equivalence g ↦ g·x₀ from G to X for any x₀ ∈ X. Theorem 0.2. Two coarse structures 𝓒₁ and 𝓒₂ on the same set X are equivalent if the following conditions are satisfied: (1) Bounded sets in 𝓒₁ are identical with bounded sets in 𝓒₂. (2) There is a coarse action ϕ₁ of a group G₁ on (X,𝓒₁) and a coarse action ϕ₂ of a...
Cofinitary and Contrafinitary Linear Groups.
Cohomologie des groupes discontinus
Cohomology of arithmetic subgroups of SL3 at infinity.
Cohomology of Congruence Subgroups of SL (n,Z).
Collineation groups of translation planes of small dimension.
Commutator subgroups of the extended Hecke groups
Hecke groups are the discrete subgroups of generated by and . The commutator subgroup of (, denoted by , is studied in [2]. It was shown that is a free group of rank . Here the extended Hecke groups , obtained by adjoining to the generators of , are considered. The commutator subgroup of is shown to be a free product of two finite cyclic groups. Also it is interesting to note that while in the case, the index of is changed by , in the case of , this number is either 4 for...
Computation of five- and six-dimensional Bieberbach groups.
Computational aspects of group extensions and their applications in topology.
Computing fundamental domains for Fuchsian groups
We exhibit an algorithm to compute a Dirichlet domain for a Fuchsian group with cofinite area. As a consequence, we compute the invariants of , including an explicit finite presentation for .
Congruence, Similarity, and Symmetries of Geometric Objects.
Congruence subgroups associated to the Monster.
Congruence subgroups of groups commensurable with of genus 0 and 1.
Constructing irreducible representations of Weyl groups.