Séminaire irrégulier

Quite recently Eliyahu Rips and Arye Juhasz constructed an Engel but not locally nilpotent group, i.e. group which satisfies for some positive $n$ the identity $underbrace{,y,dots,y]dots]}_n=e$.This group has non-postitive curvature and big commutative parts, some parts have small cancellation and some commute. - This group looks in some sense like a ring, and group multiplication behaves sometimes like multiplication and sometimes like addition. The theory of canonic forms of this group is applicable for rings, in particulary in skew field construction. In different sense some semigroup constructions can be transformed […]

The Novikov-Adian theorem states that a non-cyclic Burnside group B(m,n) of odd exponent n greater or equal 665 is infinite. Starting from the original approach, all known proofs of infiniteness of B(m,n) utilize the idea that the group can be described in terms of some iterated small cancellation condition. In the last decade, several explicit implementations of small cancellation conditions of this type were introduced which can be applied also in a more general setup to groups acting on hyperbolic metric spaces. I will give a brief overview of the […]

This talk is concerned with the space between CAT(-1) spaces and Gromov hyperbolic spaces. Part of the motivation comes from the analytic theory of hyperbolic groups, and one of the main goals is that of getting hyperbolic groups to act geometrically on hyperbolic spaces with additional CAT(-1) features. Based on joint work with Jan Spakula.