Semidensities on Odd Symplectic Supermanifolds

2000/12/27 by H. M. Khudaverdian, Hovhannes Khudaverdian, Khudaverdian, Hovhannes · 2 citations
Mathematics · Physics and Astronomy · #53A55 #53B50 #58A50 #81T70 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:53A55 #msc:53B50 #msc:58A50 #msc:81T70

paper · pdf · doi:10.48550/arxiv.math/0012256

Plain-TeX, 44 pages

arxiv created 2000/12/27 · openalex publication_date 2000/12/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 Δ-operator are used for obtaining integral invariants for (1.1)-codimensional surfaces.

Cited by

• Surface Observables, 2-Knot Invariants, and Nonabelian Electric Fluxes
• On a Grassmann odd analogue of Carrollian Manifolds

Related

• Delta-Operator on Semidensities and Integral Invariants in the Batalin-Vilkovisky Geometry
• Laplacians in Odd Symplectic Geometry
• Batalin--Vilkovisky Formalism and Odd Symplectic Geometry
• Projective Connections and Schwarzian Derivatives for Supermanifolds, and Batalin-Vilkovisky Operators
• Noncommutative differential forms and quantization of the odd symplectic category