Coverings of Complexes of Groups, with an Application to Counting Overlattices

Counting Overlattices for Polyhedral Complexes

We investigate the asymptotics of the number of “overlattices” of a cocompact lattice Γ in Aut(X), where X is a locally finite polyhedral complex. We use complexes of groups to prove an upper bound for general X, and a lower bound for certain right-angled buildings.

ALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS

Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...

Finite Groups with p-Sylow Coverings

Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks

Fuchsian groups (acting as isometries of the hyperbolic plane) occur naturally in geometry, combinatorial group theory, and other contexts. We use character-theoretic and probabilistic methods to study the spaces of homomorphisms from Fuchsian groups to symmetric groups. We obtain a wide variety of applications, ranging from counting branched coverings of Riemann surfaces, to subgroup growth an...

On subgroups of topologized fundamental groups and generalized coverings

‎In this paper‎, ‎we are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering maps‎. ‎More precisely‎, ‎we find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topology‎. ‎Moreover‎, ‎we present some conditions unde...