The Frobenius theorem for ${\mathbb{Z}}_2^n$-supermanifolds

Abstract

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

References in corpus (2)

• ${\mathbb{Z}}_2^n$-Supergeometry I: Manifolds and Morphisms
• ${\mathbb{Z}}_2^n$-Supergeometry II: Batchelor-Gawedzki Theorem

Cited by in corpus (6)

• On a ${\mathbb{Z}}_2^n$-Graded Version of Supersymmetry
• Local Forms of Morphisms of Colored Supermanifolds
• The Schwarz-Voronov Embedding of ${\mathbb{Z}}_2^n$-Manifolds
• Linear ${\mathbb{Z}}_2^n$-Manifolds and Linear Actions
• The Gelfand-Naimark-Segal construction for unitary representatins of ${\mathbb{Z}}_2^n$-graded Lie supergroups
• $N=1$ fermionic D3-branes in RNS formulation I. $C^{\infty }$-Algebrogeometric foundations of $d=4$, $N=1$ supersymmetry, SUSY-rep compatible hybrid connections, and $\hat{D}$-chiral maps from a $d=4$ $N=1$ Azumaya/matrix superspace