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Formality of hypercommutative algebras of Kähler and Cala...
[Submitted on 16 Feb 2023 (v1), last revised 24 May 2026 (this v · 2026-05-26 · via math updates on arXiv.org

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Abstract:Any Batalin-Vilkovisky algebra with a homotopy trivialization of the BV-operator gives rise to a hypercommutative algebra structure at the cochain level which, in general, contains more homotopical information than the hypercommutative algebra introduced by Barannikov and Kontsevich on cohomology. In this paper, we use the purity of mixed Hodge structures to show that the canonical hypercommutative algebra defined on any compact Calabi-Yau manifold is formal. We also study related hypercommutative algebras associated to compact Kähler and Hermitian manifolds.

Submission history

From: Geoffroy Horel [view email]
[v1] Thu, 16 Feb 2023 18:51:16 UTC (22 KB)
[v2] Fri, 24 Feb 2023 08:55:36 UTC (22 KB)
[v3] Sun, 24 May 2026 15:52:21 UTC (24 KB)