Local forms of morphisms of colored supermanifolds

Abstract

In [13], [17] and [29], we introduced the category of colored supermanifolds (Z2n-supermanifolds or just Z2n-manifolds (Z2n=Z2×…×Z2 (n times))), explicitly described the corresponding Z2n-Berezinian and gave first insights into Z2n-integration theory. The present paper contains a detailed account of parts of the Z2n-differential calculus and of the Z2n-variants of the trilogy of local theorems, which consists of the inverse function theorem, the implicit function theorem and the constant rank theorem.