Geometry of Batalin-Vilkovisky quantization (Q1308463)

An odd symplectic manifold is called a \(P\)-manifold and a \(P\)-manifold equipped with a volume element is called an \(SP\)-manifold. The author provides a complete classification of these manifolds and uses the classification to prove some results concerning the procedure of quantization introduced by \textit{I. Batalin} and \textit{G. Vilkovisky} [Phys. Lett., B 102, 27-31 (1981)].