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arXiv · 2011.01012

Linear ${\mathbb Z}_2^n$-Manifolds and Linear Actions

Andrew James Bruce·Eduardo Ibarguengoytia·Norbert Poncin
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Abstract

We establish the representability of the general linear ${\mathbb Z}_2^n$-group and use the restricted functor of points - whose test category is the category of ${\mathbb Z}_2^n$-manifolds over a single topological point - to define its smooth linear actions on ${\mathbb Z}_2^n$-graded vector spaces and linear ${\mathbb Z}_2^n$-manifolds. Throughout the paper, particular emphasis is placed on the full faithfulness and target category of the restricted functor of points of a number of categories that we are using.

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Andrew James Bruce, Eduardo Ibarguengoytia, Norbert Poncin. 2020-11-02. Linear ${\mathbb Z}_2^n$-Manifolds and Linear Actions. https://doi.org/10.3842/sigma.2021.060

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