Constructions of exotic actions on product manifolds with an asymmetric factor


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.

accepted in Kyoto Journal of Mathematics
Marek Kaluba

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