Covering abelian groups with cyclic subsets.
Covering in the set of principal ideals in the semigroup of binary relations.
Covering -groups of -groups
Covering theorems for finite non-abelian simple groups, I
Covering theorems for finite nonabelian simple groups. III. - Solutions of the equation in a finite field
Coverings in the lattice of quasivarieties of -groups.
Co-volume methods for degenerate parabolic problems.
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 Orbits and Eigenspaces of Frobenius
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.
Critical theories of varieties of semigroups satisfying a permutation identity.
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.
Cross ratios, Anosov representations and the energy functional on Teichmüller space
We study two classes of linear representations of a surface group: Hitchin and maximal symplectic representations. We relate them to cross ratios and thus deduce that they are displacing which means that their translation lengths are roughly controlled by the translations lengths on the Cayley graph. As a consequence, we show that the mapping class group acts properly on the space of representations and that the energy functional associated to such a representation is proper. This implies the existence...
Cross ratios, surface groups, and diffeomorphisms of the circle
This article relates representations of surface groups to cross ratios. We first identify a connected component of the space of representations into PSL(n,ℝ) – known as the n-Hitchin component– to a subset of the set of cross ratios on the boundary at infinity of the group. Similarly, we study some representations into associated to cross ratios and exhibit a “character variety” of these representations. We show that this character variety contains alln-Hitchin components as well as the set of...
Crossability of cancellative Kleene semigroups
Crossed modules, Crossed n-fold extension of groups and Cohomology theory in Abstract Categories