论文标题
彩色超人的局部形式
Local Forms of Morphisms of Colored Supermanifolds
论文作者
论文摘要
在\ cite {covolo：2016}，\ cite {covolo：2012}和\ cite {poncin：2016}中，我们介绍了彩色的超级曼尼福德（$ \ mathbb {z} _2 _2 _2^n $ -super \ -ma \ -ma \ -ni \ -ni \ -ni \ -folds of Colored Supermanifolds（$ \ Mathbb {Z} _ Mathbb {z} $ \ MATHBB {Z} _2^n $ -manifolds（$ \ Mathbb {z} _2^n = \ m athbb {z} _2 \ times \ times \ ldots \ times \ times \ times \ times \ times \ mathbb {z} _2 $（$ n $ times））并首先了解$ \ mathbb {z} _2^n $ integration理论。 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.
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 ($\mathbb{Z}_2^n=\mathbb{Z}_2\times\ldots\times\mathbb{Z}_2$ ($n$ 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.
