PreprintRibbon 2Knots, 1+1=2, and Duflo's Theorem for Arbitrary Lie AlgebrasDror BarNatan, Zsuzsanna Dancso, Nancy ScherichAbstractWe explain a direct topological proof for the multiplicativity of Duflo isomorphism for arbitrary finite dimensional Lie algebras, and derive the explicit formula for the Duflo map. The proof follows a series of implications, starting with "the calculation \(1+1=2\) on a 4D abacus", using the study of homomorphic expansions (aka universal finite type invariants) for ribbon 2knots, and the relationship between the corresponding associated graded space of arrow diagrams and universal enveloping algebras. This complements the results of the first author, Le and Thurston, where similar arguments using a "3D abacus" and the Kontsevich Integral were used to derive Duflo's theorem for metrized Lie algebras; and results of the first two authors on finite type invariants of wknotted objects, which also imply a relation of 2knots with Duflo's theorem in full generality, though via a lengthier path. This paper is available as a pdf (640kB) file. It is also on the arXiv: arxiv.org/abs/1811.08558.
