Normal forms of $\mathbb Z$-graded $Q$-manifolds

Alexei Kotov; Camille Laurent-Gengoux; Vladimir Salnikov

doi:10.1016/j.geomphys.2023.104908

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arXiv · 2212.05579

Normal forms of $\mathbb Z$-graded $Q$-manifolds

Alexei Kotov·Camille Laurent-Gengoux·Vladimir Salnikov

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Abstract

Following recent results of A.K. and V.S. on $\mathbb Z$-graded manifolds, we give several local and global normal forms results for $Q$-structures on those, i.e. for differential graded manifolds. In particular, we explain in which sense their relevant structures are concentrated along the zero-locus of their curvatures, especially when the negative part is of Koszul--Tate type. We also give a local splitting theorem.

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Alexei Kotov, Camille Laurent-Gengoux, Vladimir Salnikov. 2022-12-11. Normal forms of $\mathbb Z$-graded $Q$-manifolds. https://doi.org/10.1016/j.geomphys.2023.104908

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