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Multisymplectic forms of degree three in dimension seven

Bureš, JarolímVanžura, Jiří — 2003

Proceedings of the 22nd Winter School "Geometry and Physics"

A multisymplectic 3-structure on an n -dimensional manifold M is given by a closed smooth 3-form ω of maximal rank on M which is of the same algebraic type at each point of M , i.e. they belong to the same orbit under the action of the group G L ( n , ) . This means that for each point x M the form ω x is isomorphic to a chosen canonical 3-form on n . [Linear Multilinear Algebra 10, 183–204 (1981; Zbl 0464.15001)] and [Linear Multilinear Algebra 13, 3–39 (1983; Zbl 0515.15011)] obtained the classification of 3-forms...

On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes

Martin ČadekJiří Vanžura — 1998

Colloquium Mathematicae

Let ξ be an oriented 8-dimensional spin vector bundle over an 8-complex. In this paper we give necessary and sufficient conditions for ξ to have 4 linearly independent sections or to be a sum of two 4-dimensional spin vector bundles, in terms of characteristic classes and higher order cohomology operations. On closed connected spin smooth 8-manifolds these operations can be computed.

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