Group Actions on Homology Quaternionic Projective Planes

Steven H. Weintraub
1978 Proceedings of the American Mathematical Society  
A class of Z^-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 iorp = 3, or 5, infinitely many smooth manifolds of this type admit no smooth Zp -actions. Preliminaries. Notation. Throughout this paper, V denotes a 1-connected (integral) homology HP2, £ G H\ V) a
more » ... enerator. F c V is the fixed-point set of a Z^-action, and p is an odd prime. Eells and Kuiper have classified homology HP2's as follows: Theorem [5] . Let V be as above; then for some integer h, we have Px(V) = 2(2A -\% p2(V) = ([45 + 4(2/7 -l)2]/7)¿2.
doi:10.2307/2042588 fatcat:dx2jggacyfflnhmrlju3juwpkq