# Constructions of exotic actions on product manifolds with an asymmetric factor

### Abstract

We explore transformation groups of manifolds of the form $M\times S^n$, where $M$ is an asymmetric manifold, i.e. a manifold which does not admit any non-trivial action of a finite group. In particular, we prove that for $n=2$ there exists an infinite family of distinct non-diagonal effective circle actions on such products. A similar result holds for actions of cyclic groups of prime order. We also discuss free circle actions on $M\times S^1$, where $M$ belongs to the class of “almost asymmetric” manifolds considered previously by V. Puppe and M. Kreck.

Type
Publication
accepted in Kyoto Journal of Mathematics
##### Marek Kaluba
###### Mathematician

My research interests include computational algebra, geometric group theory (in particular: property (T)) and (previously) surgery aspects of manifolds.