${\mathbb O}P^2$ bundles in M-theory

Ramond has observed that the massless multiplet of11-dimensional supergravity can be generated from thedecomposition of certain representation of the exceptionalLie group $F_4$ into those of its maximal compact subgroup${\rm Spin}(9)$. The possibility of a topological originfor this observation is investigated by studying Cayleyplane, ${\mathbb O} P^2$, bundles over 11-manifolds$Y^{11}$. The lift of the topological terms givesconstraints on the cohomology of $Y^{11}$ which arederived. Topological structures and genera on $Y^{11}$ arerelated to corresponding ones on the total space $M^{27}$.The latter, being 27-dimensional, might provide a candidatefor “bosonic M-theory.” The discussion leads to aconnection with an octonionic version of Kreck–Stolzelliptic homology theory.

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Published 1 January 2009