Local Forms of Morphisms of Colored Supermanifolds

Abstract

In \cite{Covolo:2016}, \cite{Covolo:2012} and \cite{Poncin:2016}, we introduced the category of colored supermanifolds (${\mathbb{Z}}_2^n$-super\-ma\-ni\-folds or just ${\mathbb{Z}}_2^n$-manifolds (${\mathbb{Z}}_2^n={\mathbb{Z}}_2\times \dots \times {\mathbb{Z}}_2$ ($n$ times))), explicitly described the corresponding ${\mathbb{Z}}_2^n$-Berezinian and gave first insights into ${\mathbb{Z}}_2^n$-integration theory. The present paper contains a detailed account of parts of the ${\mathbb{Z}}_2^n$-differential calculus and of the ${\mathbb{Z}}_2^n$-variants of the trilogy of local theorems, which consists of the inverse function theorem, the implicit function theorem and the constant rank theorem.

arXiv comment21 pages. arXiv admin note: text overlap with arXiv:1608.00949

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Cited by in corpus (7)

• Irreducible representations of ${\mathbb{Z}}_2^2$-graded $\mathcal{N}=2$ supersymmetry algebra and ${\mathbb{Z}}_2^2$-graded supermechanics
• Integration on minimal ${\mathbb{Z}}_2^2$-superspace and emergence of space
• ${\mathbb{Z}}_2^2$-graded supersymmetry via superfield on minimal ${\mathbb{Z}}_2^2$-superspace
• Linear ${\mathbb{Z}}_2^n$-Manifolds and Linear Actions
• Comparison theorems for Kan, faintly universal and strongly universal derived functors
• Indeterminacies and models of homotopy limits
• Principal bundles in the category of ${\mathbb{Z}}_2^n$-manifolds