Deformation Quantization of Poisson Manifolds via Kontsevich Formality Theorems: A Transfinite Cohomological Approach

Mathematical Applications of Science Fiction We present a rigorous, self-contained derivation of the ex-istence of star-products on arbitrary Poisson manifolds,leveraging the full machinery of Kontsevich’s Formality The-orem. By constructing an explicit L∞-quasi-isomorphismbetween the Differential Graded Lie Algebra (DGLA) ofpolyvector fields Tpoly(M ) and the DGLA of polydifferentialoperators Dpoly(M ), we resolve the deformation quantiza-tion problem. We extend the classical analysis through atransfinite stratification of the compactified configurationspaces Cn,m, providing detailed proofs of the vanishing ofboundary integrals crucial to the Stokes’ theorem argument.This manuscript establishes the canonical bijection betweenequivalence classes of Poisson structures and star productsmodulo gauge equivalence with hyper-cohomological preci-sion.