The Frobenius theorem for $\mathbb{Z}^n_2$-supermanifolds

Tiffany Covolo; Stephen Kwok; Norbert Poncin

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arXiv · 1608.00961

The Frobenius theorem for $\mathbb{Z}^n_2$-supermanifolds

Tiffany Covolo·Stephen Kwok·Norbert Poncin

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Abstract

We continue the development of $\mathbb{Z}^n_2$-supergeometry, a natural generalization of classical ($\mathbb{Z}_2$-graded) supergeometry, by proving the Frobenius theorem for integrable distributions on differentiable $\mathbb{Z}^n_2$-supermanifolds. Both the local and global versions of the theorem are addressed.

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Tiffany Covolo, Stephen Kwok, Norbert Poncin. 2016-08-02. The Frobenius theorem for $\mathbb{Z}^n_2$-supermanifolds. https://arxiv.org/abs/1608.00961

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