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 (3)

• Local Forms of Morphisms of Colored Supermanifolds
• 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