Odd Scalar Curvature in Batalin-Vilkovisky Geometry
|Year of publication
|MU Faculty or unit
|After a brief introduction to Batalin-Vilkovisky (BV) formalism, we treat aspects of supermathematics in algebra and differential geometry, such as, stratification theorems, Frobenius theorem and Darboux theorem on supermanifolds. We use Weinstein's splitting principle to prove Darboux theorem for regular, possible degenerate, even and odd Poisson supermanifolds. Khudaverdian's nilpotent operator (which takes semidensities into semidensities of opposite Grassmann-parity) is introduced on both (i) an atlas of Darboux coordinates and (ii) in arbitrary coordinates. An odd scalar function is defined and it is shown that it has a geometric interpretation as an odd scalar curvature.