Discrete circle actions: A note using non-standard analysis
The authors prove that the existence of effective uniformly Lipschitz \(\mathbb Q/\mathbb Z\)-actions on manifolds (and some other spaces) follows from the existence of such \(\mathbb Z/n\)-actions for every \(n\). The method is non-standard analysis. The only non-trivial transformation group theoretical input is Newman's theorem. Otherwise the proof is completely elementary, taking non-standard analysis for granted. The authors give examples showing that, in contrast, there are spaces admitting no \(S^1\)-action but admitting effective actions of \(\mathbb Z/n\) for every \(n\) and hence of \(\mathbb Q/\mathbb Z\).
scientific article; zbMATH DE number 902618