Convergence groups from subgroups.
Convergence with a fixed regulator in Archimedean lattice ordered groups
Convex cocompact subgroups of mapping class groups.
Convex lines in median groups
There is proved that a convex maximal line in a median group , containing 0, is a direct factor of .
Co-rank and Betti number of a group
For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number is additive...
Correction to the paper “Generators of an orthogonal group over a finite field”
Corrigendum to: "Aspherical four-manifolds and the centres of two-knot groups".
Coset enumeration of groups generated by symmetric sets of involutions.
Counting fixed points of a finitely generated subgroup of Aff [C].
Given a finitely generated subgroup G of the group of affine transformations acting on the complex line C, we are interested in the quotient Fix( G)/G. The purpose of this note is to establish when this quotient is finite and in this case its cardinality. We give an application to the qualitative study of polynomial planar vector fields at a neighborhood of a nilpotent singular point.
Coverings in the lattice of quasivarieties of -groups.
Coxeter classes of unitary reflection groups.
Coxeter group actions on the complement of hyperplanes and special involutions
We consider both standard and twisted actions of a (real) Coxeter group on the complement to the complexified reflection hyperplanes by combining the reflections with complex conjugation. We introduce a natural geometric class of special involutions in and give explicit formulae which describe both actions on the total cohomology in terms of these involutions. As a corollary we prove that the corresponding twisted representation is regular only for the symmetric group , the Weyl groups...
Coxeter groups, Salem numbers and the Hilbert metric
Coxeter polynomials of Salem trees
We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove that if z is a root of multiplicities for the Coxeter polynomials of the trees respectively, then z is a root for the Coxeter polynomial of their join, of multiplicity at least where .
Critical constants for recurrence of random walks on -spaces
We introduce the notion of a critical constant for recurrence of random walks on -spaces. For a subgroup of a finitely generated group the critical constant is an asymptotic invariant of the quotient -space . We show that for any infinite -space . We say that is very small if . For a normal subgroup the quotient space is very small if and only if it is finite. However, we give examples of infinite very small -spaces. We show also that critical constants for recurrence can be used...
Critical percolation on certain nonunimodular graphs.
Croissance uniforme dans les groupes hyperboliques
On montre qu’un groupe hyperbolique non élémentaire est à croissance uniformément exponentielle, c’est-à-dire qu’il existe une constante strictement plus grande que 1, ne dépendant que du groupe , telle que le taux de croissance exponentiel de relatif à n’importe quel système générateur est plus grand que . On redémontre ce faisant qu’un groupe hyperbolique n’a qu’un nombre fini de classes de conjugaison de sous-groupes finis.
Cubical sets and their site.
Cubulating spaces with walls.
Curvature testing in 3-dimensional metric polyhedral complexes.