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Journal of Lie Theory 33 (2023), No. 1, 169--194
Copyright Heldermann Verlag 2023

On the Topology of J-Groups

Rafael Dahmen
Institut für Algebra und Geometrie, Fakultät für Mathematik, Karlsruher Institut für Technologie, Karlsruhe, Germany


A topological J-group is a topological group which contains an element $w$ and admits a continuous self-map $f$ 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 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 underlying space.

Keywords: Topological group, J-group, homotopy group, compact group, Lie group.

MSC: 22A05; 57T20, 22C05.

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