On Forms, Cohomology, and BV Laplacians in Odd Symplectic Geometry

Abstract

We study the cohomology of the complexes of differential, integral and pseudo forms on odd symplectic manifolds taking the wedge product with the symplectic form as differential. We show that the cohomology classes are in correspondence with inequivalent Lagrangian submanifolds and that they all define semidensities on them. Further, we introduce new operators that move from one Lagragian submanifold to another and we investigate their relation with the so-called picture changing operators for the de Rham differential. Finally, we prove the isomorphism between the cohomology of the de Rham differential and the cohomology of BV Laplacian in the extended framework of differential, integral and pseudo forms.

arXiv comment23 pages

References in corpus (11)

• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Geometry of Batalin-Vilkovisky quantization
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• On the origin of the BV operator on odd symplectic supermanifolds
• Projective Superspaces in Practice
• Supergeometry of $\Pi$-Projective Spaces
• Pictures from Super Chern-Simons Theory
• One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
• Dual Forms on Supermanifolds and Cartan Calculus
• $A_{\infty }$-Algebra from Supermanifolds
• Odd Invariant Semidensity and Divergence-like Operators on an Odd Symplectic Superspace

Cited by in corpus (3)

• On the Geometry of Forms on Supermanifolds
• A Note on Super Koszul Complex and the Berezinian
• On BV Supermanifolds and the Super Atiyah Class