We prove that the cyclic homology of a saturated \(A_\infty \) category admits the structure of a ‘polarized variation of Hodge structures’, building heavily on the work of many authors: the main point of the paper is to present complete proofs, and also explicit formulae for all of the relevant structures. This forms part of a project of Ganatra, Perutz and the author, to prove that homological mirror symmetry implies enumerative mirror symmetry.

中文翻译：

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非可交换霍奇理论中的公式

我们证明了饱和\（A_ \ infty \）类别的循环同源性在许多作者的工作基础上都承认了“霍奇结构的极化变异”的结构：本文的重点是提出完整的证明，以及所有相关结构的明确公式。这构成了Ganatra，Perutz和作者的项目的一部分，以证明同源镜对称性意味着枚举镜对称性。