Simply connected asymmetric manifolds

摘要

In this paper, we give the first examples of smooth simply connected asymmetric closed manifolds. V. Puppe has shown that there are examples of simply connected 6-manifolds on which there is no orientation-preserving nontrivial group action of a finite group. We show that all of them are actually asymmetric manifolds. The main tool in the proof is a congruence of a twisted (A) over cap -genus for certain Spin-manifolds admitting an orientation-reversing involution. This is the first restriction of this type coming from an action of a discrete group.