Abstract
A class of Z p {{\mathbf {Z}}_p} -actions, resembling well-known actions on the quaternionic projective plane, is defined and studied. The existence of such actions on a closed homology quaternionic projective plane is shown to imply numerical restrictions on the manifold’s Pontrjagin classes. One consequence is that for p = 3 p = 3 , or 5, infinitely many smooth manifolds of this type admit no smooth Z p {{\mathbf {Z}}_p} -actions.
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