Differential graded manifolds of finite positive amplitude

Kai Behrend; Hsuan-Yi Liao; Ping Xu

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arXiv · 2307.10242

Differential graded manifolds of finite positive amplitude

Kai Behrend·Hsuan-Yi Liao·Ping Xu

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Abstract

We prove that dg manifolds of finite positive amplitude, i.e. bundles of positively graded curved $L_\infty[1]$-algebras, form a category of fibrant objects. As a main step in the proof, we obtain a factorization theorem using path spaces. First we construct an infinite-dimensional factorization of a diagonal morphism using actual path spaces motivated by the AKSZ construction. Then we cut down to finite dimensions using the Fiorenza-Manetti method. The main ingredient in our method is the homotopy transfer theorem for curved $L_\infty[1]$-algebras. As an application, we study the derived intersections of manifolds.

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BibTeX RIS

Kai Behrend, Hsuan-Yi Liao, Ping Xu. 2023-07-17. Differential graded manifolds of finite positive amplitude. https://arxiv.org/abs/2307.10242

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