Abstract
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 ^ -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.
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