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arXiv · 1611.02292

On higher Dirac structures

Henrique Bursztyn·Nicolas Martinez Alba·Roberto Rubio
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Abstract

We study higher-order analogues of Dirac structures, extending the multisymplectic structures that arise in field theory. We define higher Dirac structures as involutive subbundles of $TM+\wedge^k TM^*$ satisfying a weak version of the usual lagrangian condition (which agrees with it only when $k=1$). Higher Dirac structures transversal to $TM$ recover the higher Poisson structures introduced in [8] as the infinitesimal counterparts of multisymplectic groupoids. We describe the leafwise geometry underlying an involutive isotropic subbundle in terms of a distinguished 1-cocycle in a natural differential complex, generalizing the presymplectic foliation of a Dirac structure. We also identify the global objects integrating higher Dirac structures.

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BibTeXRIS

Henrique Bursztyn, Nicolas Martinez Alba, Roberto Rubio. 2016-11-07. On higher Dirac structures. https://doi.org/10.1093/imrn%2Frnx163

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