Homotopy BV-algebras in Hermitian geometry
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909141419687936 |
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| author | Cirici, Joana Wilson, Scott O. |
| author_facet | Cirici, Joana Wilson, Scott O. |
| contents | We show that the de Rham complex of any almost Hermitian manifold carries a natural commutative $BV_\infty$-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_12314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homotopy BV-algebras in Hermitian geometry Cirici, Joana Wilson, Scott O. Algebraic Topology Differential Geometry Quantum Algebra We show that the de Rham complex of any almost Hermitian manifold carries a natural commutative $BV_\infty$-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. |
| title | Homotopy BV-algebras in Hermitian geometry |
| topic | Algebraic Topology Differential Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2403.12314 |