On the Topology of J-Groups

Abstract

We introduce the concept of a topological J-group and determine for many important examples of topological groups if they are topological J-groups or not. Besides other results, we show that the underlying topological space of a pathwise connected topological J-group is weakly contractible which is a strong and unexpected obstruction that depends only on the homotopy type of the space.

30 pages. Compared to v1 and v2, there have been some major changes; Theorem 3.13 and Corollary 3.14 are new, some of the old Open Questions are solved and some new Open Questions are added. The numbering of some theorems and questions changed. All the results in v1 and v2 still remain true