OP2 bundles in M-theory

TL;DR

This paper explores the topological and geometric structures of OP2 bundles over eleven-manifolds in M-theory, linking representation theory, cohomology constraints, and elliptic homology to propose a candidate for bosonic M-theory.

Contribution

It investigates the topological origin of supergravity multiplet decomposition via OP2 bundles and relates these structures to elliptic homology, proposing a new perspective on bosonic M-theory.

Findings

Derived cohomology constraints from topological terms.

Connected OP2 bundle structures to elliptic homology.

Proposed a 27-dimensional space as a candidate for bosonic M-theory.

Abstract

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.