On forms, cohomology and BV Laplacians in odd symplectic geometry

• Verfasst von: Catenacci, Roberto [VerfasserIn]
• Verfasst von: Cremonini, C. A. [VerfasserIn]
• Verfasst von: Grassi, Pietro A. [VerfasserIn]
• Verfasst von: Noja, Simone [VerfasserIn]
• Titel: On forms, cohomology and BV Laplacians in odd symplectic geometry
• Verf.angabe: R. Catenacci, C.A. Cremonini, P.A. Grassi, S. Noja
• E-Jahr: 2021
• Jahr: 5 April 2021
• Umfang: 32 S.
• Fussnoten: Gesehen am 02.06.2021
• Titel Quelle: Enthalten in: Letters in mathematical physics
• Ort Quelle: Dordrecht [u.a.] : Springer Science + Business Media B.V, 1975
• Jahr Quelle: 2021
• Band/Heft Quelle: 111(2021), 2, Artikel-ID 44, Seite 1-32
• ISSN Quelle: 1573-0530
• DOI: doi:10.1007/s11005-021-01384-3
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1759475130

Abstract

We study the cohomology of the complexes of differential, integral and a particular class of pseudo-forms on odd symplectic manifolds taking the wedge product with the symplectic form as a differential. We thus extend the result of Ševera and the related results of Khudaverdian-Voronov on interpreting the BV odd Laplacian acting on half-densities on an odd symplectic supermanifold. 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 a particular class of pseudo-forms.