Communications in Mathematical Physics

, Volume 247, Issue 2, pp 353–390 | Cite as

Semidensities on Odd Symplectic Supermanifolds

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Abstract

We consider semidensities on a supermanifold E with an odd symplectic structure. We define a new Δ-operator action on semidensities as the proper framework for the Batalin-Vilkovisky (BV) 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 Δ-operator are used for obtaining integral invariants for (1.1)-codimensional surfaces.

Keywords

Differential Form Symplectic Structure Integral Invariant Lagrangian Surface Proper Framework 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Science and Technology (UMIST)ManchesterUK

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