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Quantum Algebra Days / Chiara Esposito / [Formality,Reduction]=0 ? First step [Nov. 4, 2020]

 Summary

In this talk we propose a reduction scheme for multivector fields phrased in terms of L-infinity-morphisms. First, using geometric properties of the reduced manifolds we perform a Taylor expansion of multivector fields, which allows us to built up a suitable deformation retract of DGLA’s. As a second step, we contruct a Poisson analogue of Cartan model for equivariant de Rham cohomology. As a consequence we prove the existence of a curved L-infinity morphism between equivariant multivector fields and multivector fields on the reduced manifolds that coincides with the standard Marsden-Weinstein reduction.

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