Summary
Let M and N be Lagrangian submanifolds of a complex symplectic manifold S. We construct a Gerstenhaber algebra structure on \(\mathcal{T}or_\ast^{\mathcal{O}_S}(\mathcal{O}_M,\mathcal{O}_N)\) and a compatible Batalin–Vilkovisky module structure on \(\mathcal{E}xt^\ast_{\mathcal{O}_S}(\mathcal{O}_M,\mathcal{O}_N)\). This gives rise to a de Rham type cohomology theory for Lagrangian intersections.
2000 Mathematics Subject Classifications: 14C17, 16E45, 32G13, 53D12
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References
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Behrend, K., Fantechi, B. (2009). Gerstenhaber and Batalin–Vilkovisky Structures on Lagrangian Intersections. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 269. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4745-2_1
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DOI: https://doi.org/10.1007/978-0-8176-4745-2_1
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