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arXiv · 2607.01371

Categorical structures of Kuranishi spaces with $L_{\infty}[1]$-algebras

Taesu Kim
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Abstract

We introduce $L_{\infty}$-Kuranishi spaces by associating, to each chart, $L_{\infty}[1]$-algebras defined on open neighborhoods of points in the zero locus of the Kuranishi section. We show that these objects collectively form a category into which the category of smooth manifolds naturally embeds. Some notions in \cite{FOOO1} are modified to achieve the desired categorical structures; for instance, the tangent bundle condition for chart embeddings is replaced by a quasi-isomorphism condition for the $L_{\infty}[1]$-structures.

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Taesu Kim. 2026-07-01. Categorical structures of Kuranishi spaces with $L_{\infty}[1]$-algebras. https://arxiv.org/abs/2607.01371

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