On the topology of J-Groups

An abstract J-group is a purely algebraic concept that originally arose from a question concerning near-rings and state machines. In this talk I introduce the topological analog of a J-group and determine for many important classes of topological groups whether they are topological J-groups or not. Besides other results, it turns out that the underlying topological space of a pathwise connected topological J-group is always weakly contractible which is a strong and unexpected obstruction that depends only on the homotopy type of the space. Parts of this talk are joint work with Johannes Flake.