Homotopy BV-algebras in Hermitian geometry (Q6610197)

The authors associate to any almost Hermitian manifold a natural BV\(_\infty\) algebra structure (that is, a Batalin-Vilkovisky structure). The notion of BV-algebra has first been developed in the context of quantum field theory as a tool to compute path integrals in the presence of symmetry. Then, BV-algebras became very useful in the context of supermanifolds equipped with symplectic or Poisson structures, and also in algebraic topology with applications to string topology, cohomological computations, and deformation quantization. In this paper, the authors start with a review of BV-algebras and hypercommutative algebras. Then, they show that the de Rham complex of any almost Hermitian manifold carries a natural BV\(_\infty\) algebra structure satisfying the degeneration property. Examples are also studied, using Chevalley-Eilenberg algebras.