Multisymplectic 3-forms on 7-dimensional manifolds

Abstract: The goal of the paper is to give characterization of closed connected manifolds which admit a global multisympletic 3-form of some algebraic type. A generic type of such 3-form is equivalent to a G2-structure. This is the most interesting case and was solved in [Gr]. Some other algebraic types were solved quite recently. In this paper we give characterization in the remaining cases.