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arXiv · 2607.05267

The Spencer cohomology and integrability of multisymplectic structures

Manuel de León·Rubén Izquierdo-López·Manuel Lainz
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Abstract

We study the integrability problem of multisymplectic structures, by identifying them as $G$-structures. Applying the theory of Spencer cohomology, we give conditions on a multisymplectic form for it to admit a chart in which it has constant coefficients. This general study allows for a rough classification of multisymplectic structures of constant linear type, depending on the natural action of the stabilizer group. The theory is illustrated by providing a scheme for proving a Darboux theorem, which is exemplified with several relevant cases. We also build linear types of multisymplectic forms $\varpi_j$ whose flatness strictly requires a condition of order $j$. Finally, the corresponding Lie algebras are computed in the case of field theories.

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Manuel de León, Rubén Izquierdo-López, Manuel Lainz. 2026-07-06. The Spencer cohomology and integrability of multisymplectic structures. https://arxiv.org/abs/2607.05267

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