Lectures on generalized complex geometry and supersymmetry

Maxim Zabzine

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Geometric quantization and no-go theorems

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A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist....

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Super-geometric quantization.

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Locally conformal symplectic manifolds.

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Lie algebroids and mechanics

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We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold $M$ ; the set of units is the zero section identified with the manifold $M$ . We study the Legendre transformation on Lie algebroids.