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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/224810
Homotopy BV-algebras in Hermitian geometry
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We show that the de Rham complex of any almost Hermitian manifold carries a natural commutative -algebra structure satisfying the degeneration property. In the almost Kähler case, this recovers Koszul's BV-algebra, defined for any Poisson manifold. As a consequence, both the Dolbeault and the de Rham cohomologies of any compact Hermitian manifold are canonically endowed with homotopy hypercommutative algebra structures, also known as formal homotopy Frobenius manifolds. Similar results are developed for (almost) symplectic manifolds with Lagrangian subbundles.
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CIRICI, Joana and WILSON, Scott O. Homotopy BV-algebras in Hermitian geometry. Journal of Geometry and Physics. 2024. Vol. 204. ISSN 0393-0440. [consulted: 8 of June of 2026]. Available at: https://hdl.handle.net/2445/224810