Journal of Lie Theory

no. 1
On the Topology of J-Groups
Journal of Lie Theory, Volume 33 (2023) no. 1, pp. 169-194
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.
DOI: 10.5802/jolt.1279
Classification: 22A05, 57T20, 22C05
Keywords: Topological group, J-group, homotopy group, compact group, Lie group 
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     author = {R. Dahmen},
     title = {On the {Topology} of {J-Groups}},
     journal = {Journal of Lie Theory},
     pages = {169--194},
     year = {2023},
     volume = {33},
     number = {1},
     doi = {10.5802/jolt.1279},
     zbl = {1530.22001},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1279/}
}
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R. Dahmen. On the Topology of J-Groups. Journal of Lie Theory, Volume 33 (2023) no. 1, pp. 169-194. doi: 10.5802/jolt.1279

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