Constructions of exotic actions on product manifolds with an asymmetric factor

Abstract

We explore transformation groups of manifolds of the form M×Sn, where M is an asymmetric manifold, that is, a manifold which does not admit any nontrivial action of a finite group. In particular, we prove that for n=2, there exists an infinite family of distinct nondiagonal 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×S1, where M belongs to the class of “almost asymmetric” manifolds considered previously by Puppe and Kreck.