Semidensities on Odd Symplectic Supermanifolds

Details Semidensities on Odd Symplectic Supermanifolds Semidensities on Odd Symplectic Supermanifolds

2000-12-27

arxiv.org/abs/math/0012256v1

Mathematics

Differential Geometry

Plain-TeX, 44 pages

Scientific paper

We consider semidensities on a supermanifold E with an odd symplectic structure. We define a new $\Delta$-operator action on semidensities as the proper framework for Batalin-Vilkovisky formalism. We establish relations between semidensities on E and differential forms on Lagrangian surfaces. We apply these results to Batalin-Vilkovisky geometry. Another application is to (1.1)-codimensional surfaces in E. We construct a kind of pull-back of semidensities to such surfaces. This operation and the $\Delta$-operator are used for obtaining integral invariants for (1.1)-codimensional surfaces.

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