  Ramond has observed that the massless multiplet of eleven-dimensional
supergravity can be generated from the decomposition of certain representation
of the exceptional Lie group F4 into those of its maximal compact subgroup
Spin(9). The possibility of a topological origin for this observation is
investigated by studying Cayley plane, OP2, bundles over eleven-manifolds Y.
The lift of the topological terms gives constraints on the cohomology of Y
which are derived. Topological structures and genera on Y are related to the
corresponding ones on the total space M. The latter, being 27-dimensional,
might provide a candidate for `bosonic M-theory'. The discussion leads to a
connection with an octonionic version of Kreck-Stolz elliptic homology theory.
