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Group actions on homology quaternionic projective planes


Author: Steven H. Weintraub
Journal: Proc. Amer. Math. Soc. 70 (1978), 75-82
MSC: Primary 57E25
DOI: https://doi.org/10.1090/S0002-9939-1978-0515869-8
MathSciNet review: 0515869
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Abstract: A class of $ {{\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$, or 5, infinitely many smooth manifolds of this type admit no smooth $ {{\mathbf{Z}}_p}$-actions.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0515869-8
Keywords: Cyclic group actions, quaternionic projective plane
Article copyright: © Copyright 1978 American Mathematical Society

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