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arXiv · 2010.10026

Local Forms of Morphisms of Colored Supermanifolds

Tiffany Covolo·Stephen Kwok·Norbert Poncin
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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 ($\mathbb{Z}_2^n=\mathbb{Z}_2\times\ldots\times\mathbb{Z}_2$ ($n$ 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.

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BibTeXRIS

Tiffany Covolo, Stephen Kwok, Norbert Poncin. 2020-10-19. Local Forms of Morphisms of Colored Supermanifolds. https://doi.org/10.1016/j.geomphys.2021.104302

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