Derived operadic centers in deformation quantizationMPIM
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MPIM, Vivatsgasse, 7 - Seminar Room
Max Planck Institute for Mathematics
Abstract Homotopy Theory Seminar
It is well known that Hochschild cohomology and, in particular, the algebraic structure it carries, plays a central role in studying the infinitesimal noncommutative deformations of geometric spaces. We construct a canonical solution to Deligne’s conjecture for Hochschild cochains on a scheme, even for the singular case, by exhibiting the Hochschild complex as an ∞-operadic center. We show that this equips the Hochschild complex with a universal E2-algebra structure that precisely agrees with the classical Gerstenhaber bracket and cup product on cohomology in the affine and smooth cases. Our motivation stems from the mysterious appearance of the square root of the Todd genus in Kontsevich’s formality theorem in deformation quantization, as well as the conjectural relationships between these objects and the motivic Galois group.