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arXiv · 1512.02810

Introduction to graded geometry

Maxime Fairon
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Abstract

This paper aims at setting out the basics of $\mathbb{Z}$-graded manifolds theory. We introduce $\mathbb{Z}$-graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric algebra to define functions is made clear. Moreover, we define vector fields and exhibit their graded local basis. The paper also reviews some correspondences between differential Z-graded manifolds and algebraic structures.

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Maxime Fairon. 2015-12-09. Introduction to graded geometry. https://doi.org/10.1007/s40879-017-0138-4

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