Foldable cubical complexes of nonpositive curvature.
Folding on the wedge sum of graphs and their fundamental group.
Følner sequences in polycyclic groups.
The isoperimetric inequality |∂Ω| / |Ω| = constant / log |Ω| for finite subsets Ω in a finitely generated group Γ with exponential growth is optimal if Γ is polycyclic.
Folner sets of alternate directed groups
An explicit family of Folner sets is constructed for some directed groups acting on a rooted tree of sublogarithmic valency by alternate permutations. In the case of bounded valency, these groups were known to be amenable by probabilistic methods. The present construction provides a new and independent proof of amenability, using neither random walks, nor word length.
For Coxeter groups is a coefficient of a uniformly bounded representation
We prove the theorem in the title by constructing an action of a Coxeter group on a product of trees.
Formal language theory and the geometry of 3-manifolds.
Four series of hyperbolic space groups with simplicial domains, and their supergroups
Fox pairings and generalized Dehn twists
We introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group algebras of the fundamental groups of surfaces. This work is inspired by the Kawazumi–Kuno generalization of the Dehn twists to non-simple closed curves on surfaces.
Framed Links for Pfeiffer Identities.
Free and non-free subgroups of the fundamental group of the Hawaiian Earrings
The space which is composed by embedding countably many circles in such a way into the plane that their radii are given by a null-sequence and that they all have a common tangent point is called “The Hawaiian Earrings”. The fundamental group of this space is known to be a subgroup of the inverse limit of the finitely generated free groups, and it is known to be not free. Within the recent move of trying to get hands on the algebraic invariants of non-tame (e.g. non-triangulable) spaces this space...
Free burnside semigroups
This paper surveys the area of Free Burnside Semigroups. The theory of these semigroups, as is the case for groups, is far from being completely known. For semigroups, the most impressive results were obtained in the last 10 years. In this paper we give priority to the mathematical treatment of the problem and do not stress too much neither motivation nor the historical aspects. No proofs are presented in this paper, but we tried to give as many examples as was possible.
Free Burnside Semigroups
This paper surveys the area of Free Burnside Semigroups. The theory of these semigroups, as is the case for groups, is far from being completely known. For semigroups, the most impressive results were obtained in the last 10 years. In this paper we give priority to the mathematical treatment of the problem and do not stress too much neither motivation nor the historical aspects. No proofs are presented in this paper, but we tried to give as many examples as was possible.
Free group automorphisms, invariant orderings and topological applications.
Free group languages : rational versus recognizable
We provide alternative proofs and algorithms for results proved by Sénizergues on rational and recognizable free group languages. We consider two different approaches to the basic problem of deciding recognizability for rational free group languages following two fully independent paths: the symmetrification method (using techniques inspired by the study of inverse automata and inverse monoids) and the right stabilizer method (a general approach generalizable to other classes of groups). Several...
Free group languages: Rational versus recognizable
We provide alternative proofs and algorithms for results proved by Sénizergues on rational and recognizable free group languages. We consider two different approaches to the basic problem of deciding recognizability for rational free group languages following two fully independent paths: the symmetrification method (using techniques inspired by the study of inverse automata and inverse monoids) and the right stabilizer method (a general approach generalizable to other classes of groups). Several...
Free products with amalgamation of finite groups and finite outer automorphism groups of free groups
Free quotients of finitely presented groups.
Frobenius groups generated by two elements of order 3.
Fully commutative Kazhdan-Lusztig cells
We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generalized version of the Temperley-Lieb algebra.
Fundamental central dispersion in a simple system