
Journal of Lie Theory 33 (2023), No. 1, 169194 Copyright Heldermann Verlag 2023 On the Topology of JGroups Rafael Dahmen Institut für Algebra und Geometrie, Fakultät für Mathematik, Karlsruher Institut für Technologie, Karlsruhe, Germany rafael.dahmen@kit.edu [Abstractpdf] A topological Jgroup is a topological group which contains an element $w$ and admits a continuous selfmap $f$ such that $f(x\cdot w)=f(x)\cdot x$ holds for all $x$. We determine for many important examples of topological groups if they are topological Jgroups or not. Besides other results, we show that the underlying topological space of a pathwise connected topological Jgroup is weakly contractible which is a strong and unexpected obstruction that depends only on the homotopy type of the underlying space. Keywords: Topological group, Jgroup, homotopy group, compact group, Lie group. MSC: 22A05; 57T20, 22C05. [ Fulltextpdf (192 KB)] for subscribers only. 