Related papers: A Note on Trimedial Quasigroups

We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic…

The aim of this short note is to establish a 2-equivalence between a certain 2-category of foams and that of singular Soergel bimodules of type A.

The goal of this note is to construct, on many manifolds, non-trivial concordances from the identity to itself. This produces counterexamples to a recent conjecture by Botvinnik.

We prove that, for any prime $p$, there are precisely $2p^4-p^3-p^2-3p-1$ medial quasigroups of order $p^2$, up to isomorphism.

The aim of this paper is to study quasitriangular structures on a class of semisimple Hopf algebras constructed through abelian extensions of $Z_2$ for an abelian group $G$. We prove that there are only two forms of them. Using such…

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…

Among connected linear algebraic groups, quasi-reductive groups generalize pseudo-reductive groups, which in turn form a useful relaxation of the notion of reductivity. We study quasi-reductive groups over non-archimedean local fields,…

We improve a result of Prokhorov and Shramov on the rank of finite $p$-subgroups of the birational automorphism group of a rationally connected variety. Known examples show that they are sharp in many cases.

We prove a partial regularity result for local minimizers of quasiconvex variational integrals with general growth. The main tool is an improved A-harmonic approximation, which should be interesting also for classical growth.

The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.

The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.

This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…

We obtain a criterion for quasiconvexity of a subgroup of an amalgamated free product of two word hyperbolic groups along a virtually cyclic subgroup. The result provides a method of constructing new word hyperbolic group in class (Q), that…

The purpose of this short note was to outline the current status, then in 2011, of some research programs aiming at a categorification of parts of A.Connes' non-commutative geometry and to provide an outlook on some possible subsequent…

The aim of the note is to extend the uniformization theorem to compact Kahler spaces X with mild singularities and establish a kind of rigidity of their universal coverings. We assume the fundamental group of X is large, residually finite…

Bowditch showed that a one-ended hyperbolic group which is not a triangle group splits over a two-ended group if and only if its boundary has a local cut point. As a corollary one obtains that splittings of hyperbolic groups over two-ended…

In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.

In this paper, we present a notion of quasiconvexity in the setting of finitely-generated groups with hyperbolically embedded subgroups. Our main result shows that this notion yields uniform quasiconvex constants in the setting of coned-off…

Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.

We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction…