XXV Workshop on Geometric Methods in Physics | 2-8.07.2006 | |||||

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## Theodore Voronov## Differential forms and odd symplectic geometryWe show that classical differential-geometric objects such as differential forms on a manifold M possess "hidden symmetries" making them objects of odd symplectic geometry. They admit a natural action of the supergroup of all canonical transformations of the anticotangent bundle ΠT ^{*}M. The Batalin-Vilkovisky
operator (the odd Laplacian on half-densities) from this viewpoint is
just the de Rham differential considered with such extra symmetry.
An underlying fact is a simple remark from linear algebra
concerning the Berezinian of a symplectic transformation. We discuss this and other relations between classical geometry and odd brackets. Based on a joint work with H. Khudaverdian. |