Projective Connections and Schwarzian Derivatives for Supermanifolds, and Batalin-Vilkovisky Operators

2009/09/29 by Jacob George, George, Jacob · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.0909.5419

11 pages, no figures

arxiv created 2009/09/29 · openalex publication_date 2009/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the notion of a Thomas projective connection (a projective equivalence class of linear connections) for supermanifolds. As a by-product, we arrive at a generalisation of the multidimensional Schwarzian derivative for the super case which was previously unknown. This is combined with our previous construction of a Laplacian on the algebra of densities for a projectively connected manifold and allows us to study Batalin-Vilkovisky type operators and the relation between projective connections and odd Poisson structures.

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• Natural and Projectively Invariant Quantizations on Supermanifolds

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