Discrete circle actions: A note using non-standard analysis

Larry M. Manevitz, Shmuel Weinberger

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this note we prove that the existence of effective uniformly Lipschitz ℚ/ℤ actions on manifolds (and other spaces) follows from the existence of such Zn actions. The method of approach is non-standard analysis with all non-trivial transformation group theoretical information concentrated in Newman's theorem; this results in a completely elementary argument. We give examples showing that, in contrast, there are spaces with no S1 effective actions despite Zn and hence ℚ/ℤ effective actions.

Original languageEnglish
Pages (from-to)147-155
Number of pages9
JournalIsrael Journal of Mathematics
StatePublished - 1996
Externally publishedYes


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