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ALT

Seminar

Three-dimensional topological field theory anda categorification of the derived category of coherent sheaves

Kapustin, A (CALTECH)
Saturday 18 April 2009, 12:00-13:00

Satellite

Abstract

The Rozansky-Witten model is a 3d topological sigma-model whose target space X is a complex symplectic manifold. I will describe the 2-category structure on the set of its boundary conditions and show that it is a categorification of the derived category of coherent sheaves on X. In the special case when X is a cotangent bundle to a complex manifold Y, this 2-category is closely related to the 2-category of derived categorical sheaves over Y introduced by Toen and Vezzosi. I will also explain a surprising connection between a categorification of deformation quantization and complex symplectic geometry.

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