On forms, cohomology and BV Laplacians in odd symplectic geometry

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 interpreti...

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Bibliographic Details
Published in:Letters in mathematical physics 2021-04, Vol.111 (2), Article 44
Main Authors: Catenacci, R., Cremonini, C. A., Grassi, P. A., Noja, S.
Format: Article
Language:English
Subjects:
Complex Systems
Differential geometry
Geometry
Group Theory and Generalizations
Homology
Integrals
Isomorphism
Manifolds (mathematics)
Mathematical and Computational Physics
Operators (mathematics)
Physics
Physics and Astronomy
Theoretical
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Summary: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.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-021-01384-3